1087 1367 assume 1367 1547 that 1547 1627 your 1627 1927 doctor 1927 2247 tells 2247 2347 you 2347 2507 that 2507 3107 specific 3107 3487 medical 3487 3747 test 3747 4087 came 4087 4227 up 4227 4877 positive 5047 5827 question 5827 7307 always 7307 7487 or 7487 7627 are 7627 7767 you 7767 8397 not 8567 9147 it's 9147 9387 not 9387 9527 as 9527 10667 simple 10667 10687 as 10687 10707 it 10707 11667 sounds 11837 12717 like 12717 13957 of 13957 15157 statistics 15157 15837 stochastics 15837 16277 involved 16277 17397 here 17397 17537 and 17537 17717 so 17717 17957 get 17957 18537 some 18537 18957 medical 18957 20977 tests 20977 21217 for 21217 22407 instance 22577 22937 this 22937 23417 test 23417 23677 could 23677 24657 have 24657 24797 the 24797 25877 following 25877 26857 properties 26857 26957 the 26957 27757 probability 27757 27977 of 27977 28097 the 28097 28557 test 28557 28837 given 28837 29057 the 29057 29517 positive 29517 30347 result 30517 30857 when 30857 31237 you 31237 32557 is 32557 32837 could 32837 33157 be 33157 33337 for 33337 34057 instance 34057 34377 ninety 34377 35417 percent 35417 36127 on 36297 36817 in 36817 36937 the 36937 37677 probability 37677 37837 of 37837 37957 the 37957 38857 test 38857 39137 giving 39137 39237 the 39237 39857 negative 39857 40337 results 40337 40477 when 40477 40637 you're 40637 42117 real 42117 42557 is 42557 42857 point 42857 43457 number 43457 43777 these 43777 44097 two 44097 44697 guys 44697 44997 to 44997 45317 some 45317 45477 two 45477 45877 number 45877 46337 cost 46337 46537 number 46537 46777 hundred 46777 47877 percent 47877 48177 either 48177 48817 your 48817 49157 tested 49157 49757 positive 49757 50117 or 50117 50637 tested 50637 51337 negative 51337 51757 period 54654 55874 assume 55874 56654 furthermore 56654 57504 that 57637 58317 healthy 58317 59417 people 59550 60050 are 60050 60510 only 60510 60910 tested 60910 61710 positive 61710 62490 in 62490 62850 very 62850 63110 very 63110 64010 few 64010 64590 cases 64590 65330 hopefully 65330 65550 going 65550 65650 to 65650 65870 see 65870 66070 what 66070 66270 this 66270 68090 means 68090 68270 that 68270 68430 say 68430 68630 this 68630 69330 mobility 69330 70070 is 70070 70590 pronoun 70590 70930 part 70930 71250 in 71250 72310 thousands 72443 73163 among 73163 73303 number 73303 74343 thousand 74343 74363 and 74363 74383 three 74383 75303 persons 75436 76176 pronoun 76176 76376 baby 76376 76836 tested 76836 77536 positive 77669 78209 and 78209 78249 the 78249 79169 remaining 79169 79289 nine 79289 79829 hundred 79829 79849 and 79849 80729 nineteen 80862 81822 nine 81955 82475 to 82475 82515 be 82515 83655 tested 83788 85048 negative 85181 86001 things 86001 86201 should 86201 86581 be 86714 86974 that 86974 87154 this 87154 87334 should 87334 87454 be 87454 88074 positive 88074 88954 for 88954 89254 determiner 89254 89714 person 89714 90134 to 90134 90234 be 90234 91314 negative 91314 91654 for 91654 92014 healthy 92014 92864 persons 92997 93437 these 93437 94017 quantities 94017 94597 your 94597 95277 conditional 95277 96237 probabilities 96237 96537 is 96537 96577 determiner 96577 97257 condition 97257 97807 given 97940 98360 on 98360 98460 the 98460 99000 condition 99000 99260 that 99260 99440 you 99440 100120 are 100253 100693 what's 100693 101013 the 101146 101986 vapidity 101986 102186 that 102186 102346 you 102346 103186 just 105537 106077 the 106077 106637 data 106637 106817 in 106817 106897 the 106897 107017 on 107017 107097 the 107097 108337 population 108945 110605 assume 110605 111225 that's 111833 112033 the 112033 112773 probability 112773 112913 of 112913 113353 somebody 113353 113633 being 113633 114193 healthy 114193 114773 is 115381 115861 over 115861 116201 point 116201 116601 nine 116601 116981 nine 116981 117341 nine 117341 117781 nine 117781 118681 nine 118681 118841 so 118841 119021 it's 119021 119401 really 119401 119501 determiner 119501 119761 rare 119761 120641 disease 120641 120801 in 120801 121101 dealing 121101 121641 with 122249 122889 the 122889 123369 ability 123369 123489 of 123489 124409 somebody 124409 124829 being 124829 125499 in 126107 126207 the 126207 126987 opposite 126987 127107 number 127107 127707 minus 127707 127827 this 127827 127947 number 127947 128287 hundred 128287 128827 percent 128827 129207 minus 129207 129567 ninety 129567 130027 nine 130635 131155 point 131155 131335 nine 131335 131495 nine 131495 132255 nine 132255 132935 percent 133543 134203 that's 134811 135311 point 135311 135411 oh 135411 136311 oh 136311 136771 oh 137379 138019 number 141705 142905 no 143103 143643 that's 143643 143963 dude 143963 144123 with 144123 144183 the 144183 145143 computation 145143 145643 with 145643 146163 some 146163 146743 actual 146743 147483 numbers 147483 147743 of 147743 148423 persons 148423 148723 let's 148723 149143 assume 149143 149323 that 149323 149423 you 149423 149543 have 149543 149583 determiner 149583 150403 population 150403 151223 of 151421 151981 number 151981 152261 hundred 152261 152581 million 155305 157605 then 157605 157625 this 157625 157965 fraction 158421 159061 is 159061 159721 healthy 159721 159961 so 159961 160201 that 160201 160481 would 160481 160981 be 160981 161401 ninety 161401 161621 nine 161621 162641 million 162641 162881 nine 162881 163121 hundred 163121 163381 ninety 163381 163581 nine 163581 164861 thousand 164861 165401 these 165401 166241 are 166241 166481 the 166481 167721 people 167721 167821 the 167821 168741 rest 169197 169577 is 169577 170457 in 170457 170737 these 170737 170857 are 170857 171057 not 171057 171177 too 171177 172137 many 172137 172397 it's 172397 172977 just 172977 173717 CO 173717 174057 point 174057 174357 oh 174357 174757 oh 174757 174917 oh 174917 175457 oh 175457 176437 number 176437 177077 times 177077 177237 number 177237 177537 hundred 177537 178277 million 178733 179213 number 179213 179713 thousand 181738 182638 among 182638 183058 the 183058 183478 ahead 183478 183758 of 183758 185338 the 185338 187358 people 187358 187578 how 187578 187898 many 187898 187998 are 187998 188258 going 188258 188378 to 188378 188498 be 188498 189338 tested 189338 190118 positive 190118 190298 and 190298 191238 see 191238 191458 if 191458 191618 you 191618 191778 are 191778 192098 and 192098 192938 see 192938 193118 if 193118 193298 you're 193298 194278 healthy 194278 194438 they 194438 194858 have 194858 194958 determiner 194958 195538 chance 195538 196148 of 196667 197247 old 197247 197547 point 197547 197707 number 197707 198647 percent 199166 199526 being 199526 199886 tested 199886 200526 positive 200526 201266 so 201266 201846 opened 201846 202026 number 202026 202546 percent 202546 202746 of 202746 202926 the 202926 203266 eessa 203266 203706 tested 203706 204266 positive 204266 204546 which 204546 205146 is 205146 205526 ninety 205526 205766 nine 205766 206386 thousand 206386 206626 nine 206626 206966 hundred 206966 207306 ninety 207306 207986 nine 208505 209285 these 209285 209365 are 209365 209885 false 209885 210685 positives 211204 211824 they 211824 212064 should 212064 212284 not 212284 212404 be 212404 212824 tested 212824 214304 positive 214304 214444 they 214444 214644 should 214644 214744 be 214744 215104 tested 215104 215544 negative 215544 215904 because 215904 216124 there 216124 216504 is 216504 216604 determiner 216604 217244 syllabus 217244 218144 force 218144 219104 positives 219104 219264 the 219264 220384 rest 220384 220604 which 220604 220704 is 220704 220804 the 220804 221444 majority 221444 222264 luckily 222783 223043 is 223043 223823 tested 224342 225662 negative 226181 226661 oh 226661 226961 point 226961 227241 nine 227241 227661 nine 227661 227941 nine 227941 228161 nine 228161 228721 nine 228721 229141 times 229141 229501 these 229501 229901 ninety 229901 230121 nine 230121 230481 million 230481 230961 nine 230961 231141 ninety 231141 231341 nine 231341 232151 thousand 232670 233030 which 233030 233450 is 233450 233770 ninety 233770 234050 nine 234050 234950 million 235469 236049 eight 236049 236309 hundred 236309 236589 ninety 236589 236769 nine 236769 237889 thousand 238408 239028 and 239028 239588 number 240107 240547 these 240547 240567 are 240567 241047 tested 241047 241827 negative 241827 241887 this 241887 242007 is 242007 242187 as 242187 242287 it 242287 242527 should 242527 242927 be 243446 243686 the 243686 244046 test 244046 244266 comes 244266 244386 out 244386 245146 negative 245665 247045 for 247045 247105 the 247105 247725 people 247725 247845 with 247845 248365 some 248884 250164 exceptions 250683 251083 now 251083 251383 the 251383 251763 person 251763 252063 s 255192 255852 how 255852 256152 many 256152 256172 are 256172 256772 tested 256772 257272 positive 258814 259174 ninety 259174 259714 percent 259714 259874 of 259874 260194 the 260194 260754 persons 260754 260834 are 260834 261214 tested 261214 262394 positive 262760 263340 which 263340 263440 is 263440 263680 nine 263680 264300 hundred 264300 264320 if 264320 264420 you 264420 264920 start 264920 265040 with 265040 265240 number 265240 265980 thousand 266346 267186 the 267186 267806 remaining 267806 267966 number 267966 270606 hundred 270606 270906 ninety 270906 271126 number 271126 271626 hundred 271626 271886 which 271886 272286 is 272286 272586 these 272586 272806 ten 272806 274186 percent 274186 274486 off 274486 274786 once 274786 275946 negatives 275946 276086 the 276086 276446 test 276446 276726 comes 276726 276986 out 276986 277876 negative 278242 278542 but 278542 278662 it 278662 279452 shouldn't 279818 280458 these 280458 280838 guys 280838 280918 are 280918 281198 really 284461 284901 now 284901 284921 we 284921 285121 can 285121 286181 compute 286501 286841 the 286841 287741 probability 287741 287761 that 287761 287781 is 287781 287801 of 287801 288301 interest 288301 288321 to 288321 288841 us 289161 290201 namely 290521 291641 that's 291641 292241 another 292241 292821 conditional 292821 293921 probability 293921 294121 but 294121 294301 it's 294301 294401 the 294401 294941 conditional 294941 295801 probability 295801 297441 of 297441 298481 what's 298481 298581 the 298581 299421 chances 299421 300141 are 300141 300961 you 301281 302381 being 302381 302941 ill 303261 303501 if 303501 303661 you 303661 303901 want 303901 304521 tested 304521 305431 positive 305751 306251 that 306251 306491 way 306491 307121 round 309209 309449 so 309449 310209 before 310209 310369 the 310369 310809 data 310809 311009 that 311009 311109 we 311109 311429 had 311429 311689 was 311689 311869 the 311869 312149 other 312149 312369 way 312369 312749 wrong 312749 313009 what's 313009 313129 the 313129 313629 chances 313629 314009 of 314009 314309 being 314309 315289 positive 315552 316432 if 316695 317035 you 317035 317235 are 317235 317835 determiner 318098 318898 no 319161 320421 condition 320421 320721 has 320984 322104 changed 322367 323157 you 325450 326210 so 326210 326230 we 326230 327310 can 327318 327658 do 327658 327738 the 327738 328258 numbers 332124 332464 it's 332464 332724 on 332724 332744 the 332744 333824 condition 334128 334508 that 334508 334728 you 334728 335108 tested 335108 335688 positive 335688 336668 so 336668 336788 the 336788 337048 only 337048 337348 people 337348 337508 that 337508 337588 you 337588 337828 have to 337828 338028 look 338028 338508 at 338508 338688 uhhh 338688 339048 these 339048 339268 nine 339268 339968 hundred 340272 340592 and 340592 342072 these 342376 342896 ninety 342896 343116 nine 343116 343556 thousand 343556 343816 nine 343816 344016 hundred 344016 344336 ninety 344336 344986 nine 346824 347324 we 347324 347804 have to 347804 348564 check 349154 349774 which 349774 350894 fraction 350894 350914 of 350914 351714 these 352304 352764 is 352764 353264 actually 353264 354384 ill 354384 354624 and 354624 355524 that's 355524 356204 these 356204 356404 nine 356404 360824 hundred 360824 361764 so 361764 362104 that's 362104 362204 the 362204 363344 probity 363934 364694 looking 364694 365294 for 365884 366324 how 366324 367924 many 367924 368584 restriction 368584 368744 pronoun 368744 368944 should 368944 369064 be 369064 369544 saying 369544 369764 which 369764 370324 fraction 370324 370524 of 370524 370624 the 370624 371244 persons 371244 371404 were 371404 371804 tested 371804 372584 positive 372584 373284 are 373284 374184 really 374184 374764 ill 374764 375424 actually 375424 376014 determiner 376604 377004 this 377004 377954 fiction 378544 379484 and 379484 379784 since 379784 379924 it 379924 380264 dealing 380264 380584 with 380584 380744 the 380744 381404 abilities 381404 381564 they 381564 382264 can 382264 382584 do 382584 382864 very 382864 384724 course 384724 385604 computations 385604 385784 that 385784 386084 say 386084 386264 this 386264 386624 is 386624 387124 about 387124 387404 number 387404 388204 thousand 388204 388824 divided 388824 389604 by 390194 390954 well 391544 392004 number 392004 392324 hundred 392324 393064 thousand 393654 394254 just 394254 394554 the 394554 394814 order 394814 394914 of 394914 395394 magnitude 395394 396054 five 396644 398064 scans 398064 398284 three 398284 399084 zeros 399084 399364 and 399364 399744 then 399744 399844 we 399844 400184 get 400184 400304 to 400304 400524 this 400524 400904 is 400904 401184 pronoun 401184 401764 over 401764 402524 hundred 403114 403494 number 403494 404094 percent 404094 404674 open paren 404674 404834 oh 404834 405754 number 405754 406534 so 407124 408304 given 408304 408544 that 408544 408724 you 408724 409084 tested 409084 410564 positive 410564 411044 your 411044 411644 morbidity 411644 411884 of 411884 412264 being 412264 412564 in 412564 412964 his 412964 413344 number 413344 414524 percent 415114 416014 which 416014 416074 is 416074 416394 not 416394 416534 that 416534 416854 much 420649 420749 of 420749 421249 course 421249 421429 that 421429 421929 depends 421929 422149 on 422149 422249 the 422249 422589 date 422589 422749 of 422749 422849 the 422849 423529 tree 423803 424283 and 424283 424443 that 424443 425193 here 425467 425887 if 425887 426107 these 426107 426387 dates 426387 426487 are 426487 426967 different 426967 427027 is 427027 427147 the 427147 427587 result 427587 427767 can 427767 428247 be 428247 428587 pretty 428587 429047 different 429047 431367 to 431641 432421 know 432421 432641 the 432641 433041 outcome 433041 434221 but 434221 434741 something 434741 435301 that's 435301 435721 general 435721 436321 interest 436321 436461 in 436461 439861 general 439861 440461 this 440461 441061 formula 441061 441341 looks 441341 441641 like 441641 441741 the 441741 442421 following 442421 442501 pronoun 442501 442741 need 442741 443221 to 443495 444595 decline 444595 445735 the 446009 447669 old 447669 448209 okay 448209 448529 so 448529 448869 what 448869 449029 do 449029 449169 we 449169 449609 have 449609 449849 in 449849 450569 the 450843 451843 numerator 451843 452003 on 452003 452343 these 452343 452623 nine 452623 453043 hundred 453043 453483 twelve 453483 453623 that 453623 453803 they 453803 454043 come 454043 454713 from 454987 455487 this 455487 455687 was 455687 455887 the 455887 456407 total 456407 456827 number 456827 456847 of 456847 457687 persons 457961 458801 times 458801 458921 the 458921 459781 probability 459781 460001 of 460001 460281 being 460281 461461 in 461461 461821 times 461821 462281 the 462281 462961 conditional 462961 464501 probability 464501 464981 of 464981 465221 being 465221 465521 tested 465521 466321 positive 466321 466621 if 466621 466821 you 466821 468131 are 470303 470563 so 470563 470823 we've 470823 471763 got 471763 472223 total 472223 472623 number 472623 472743 of 472743 473483 persons 473483 474343 times 474343 474863 ability 474863 476063 of 476509 477289 times 477289 477569 the 477569 478729 conditional 478729 479569 probability 480015 480295 of 480295 480615 being 480615 482055 disappointed 482055 482095 if 482095 482295 you 482295 482815 are 484765 485165 same 485165 485485 number 485485 486225 PS 486225 487625 downstairs 487625 488425 copy 488768 489428 conditional 489428 490288 probability 490288 490708 times 490708 491168 the 491168 492108 ability 492451 493351 times 493351 493371 the 493371 493671 total 493671 494311 number 494311 495231 plus 495574 495774 and 495774 496034 now 496034 496814 these 496814 497314 ninety 497314 497554 nine 497554 498014 thousand 498014 498254 nine 498254 498494 hundred 498494 498774 ninety 498774 499274 nine 501379 503239 we 503239 503699 start 503699 503719 with 503719 503779 the 503779 504279 total 504279 504659 number 504659 505759 multiply 505781 506041 the 506041 506961 probability 506961 506981 of 506981 507221 being 507221 508701 healthy 508701 508841 and 508863 509623 multiplied 509623 509783 by 509783 509883 the 509883 510583 condition 510583 510823 of 510823 510923 the 510923 511403 ability 511403 511523 of 511523 511783 being 511783 512183 tested 512183 513093 positive 513115 513555 if 513555 513695 you 513695 514675 are 516255 516815 so 516815 517175 this 517175 517395 is 517395 517935 the 517935 518415 total 518415 518915 number 518915 518955 of 518955 519315 times 519315 519435 the 519435 520175 probability 520175 520335 of 520335 520595 being 520595 521535 healthy 521535 521915 times 521915 522075 the 522075 522935 conditional 522935 524345 probability 524617 524957 of 524957 525237 being 525237 525677 tested 525677 526657 positive 526657 526777 if 526777 526937 you 526937 527417 are 527689 528449 anything 528721 530041 and 530041 530221 we 530221 530441 can 530441 530941 cancel 530941 531661 the 531661 532001 total 532001 532301 number 532301 532441 of 532441 532961 persons 532961 533711 you 533983 534343 can 534343 534663 just 534663 534883 get 534883 535183 some 535183 535503 phone 535503 535763 line 535763 537223 voting 537223 538563 some 538563 539103 sorts 539103 539663 of 539663 542683 probabilities 542683 543163 closely 543163 543283 you 543283 543563 see 543563 543803 that 543803 544523 the 544523 545863 abilities 545863 546323 occurring 546323 546383 in 546383 546883 this 546883 548023 equation 548295 549075 after 549075 549815 class 549815 550055 on 550055 550135 the 550135 550675 left-hand 550675 551735 side 551735 551955 they 551955 552075 are 552075 552535 being 552535 553575 conditioned 553575 553895 on 553895 554255 being 554255 555015 ill 555015 555215 or 555215 555455 being 555455 556795 healthy 556795 556975 and 556975 557215 our 557215 557795 results 557795 558265 is 558537 558997 just 558997 559017 the 559017 559257 other 559257 559457 way 559457 560157 around 560429 561089 period 561089 561929 probabilities 561929 562209 the 562209 562569 validity 562569 562689 of 562689 563069 being 563069 563549 ill 563549 563689 and 563689 563849 it's 563849 564449 conditioned 564449 565099 on 565371 565771 being 565771 566131 tested 566131 566711 positive 566711 566991 so 566991 567211 this 567211 567391 is 567391 567471 an 567471 567991 equation 567991 568191 that 568191 568531 allows 568531 568771 us 568771 569391 to 569391 570091 invert 570091 570271 the 570271 570971 auto 570971 571501 you 571773 572533 inside 572533 573853 the 573853 574333 condition 574333 574553 of 574553 576113 ability 576113 576313 this 576313 576453 is 576453 576813 called 576813 578153 space 578153 580113 theater