Sometimes misleading inferences can be drawn if one fails to think carefully about the appropriate conditional probability. In the 1980s in the US, there was a good deal of discussion about the epidemic of teenage pregnancy, and programs were established to combat the problem. Part of the evidence used to support this view was the fact that the proportion of infants whose mothers were teenagers was rising, from 14.0% in 1960 to 18.9% in 1975 a dramatic rise of 35% in only 15 years. These proportions are conditional probabilities. That is, given a birth (B), these are the probabilities that the mother was under age 20 (T):

1. Obtain the number of births to women younger than 20 years old and women age 20 or older in 1960 and 1975 from Table 83 in the 1986 Statistical Abstract (see attached at the end).
2. calculate

C. Discuss the evidence for an epidemic of teenage pregnancy. Explain why the inferences drawn from the conditional probabilities in the first paragraph may be misleading.

Pr(T|B&1960) = 0.140 Pr(T|B&1975) = 0.189 Drawing data from the 1981 and 1985 US Statistical Abstract, the number of reproductive age (10-49) in the US wasik Age 1960 19752 10-192 14,835,000 19,494,000 20-494 35,015,000+ 43,705,000 Using the notation:- B =birth during year T =woman aged 10-194 ~T=woman aged 20-494 (b) Calculate: Pr(T|1960), Pr(~7|1960) Pr(B|T&1960), Pr (B|~T&1960) Pr(T|1975), Pr (~1|1975) Pr(B|T&1975), Pr (B|-T&1975)- Births and Birth Rates 57 No. 83. BIRTHS AND BIRTH RATES: 1960 TO 1983 [Births in thousands, except as indicated. Beginning 1970, excludes births to nonresidents of U.S. See Appendix Ill. Minus sign (-) indicates decrease. For population bases used to derive these data, see text, p. 54. See also Historical Statistics, Colonial Times to 1970, series B 1, B 5-10, and B 12-20] ITEM 1960 1965 1970 1975 1976 1977 1978 1979 1980 1981 1982 1983 Live births 4,258 3,760 3,731 3,144 3,168 3,327 3,333 3,494 3,612 3,629 3,681 3,639 Average annual percent change .8 - 2.5 -2 -3.4 .8 5.0 2 4.8 3.4 .5 11.4-1.1 White..... 3,601 3,124 3,091 2,552 2,568 2,691 2,681 2,808 2.899 2,809 2,942 2,904 Black and other 657 636 640 592) 600 636 652 686 714 721738 735 Black... 602 581 572 512 514 544 652 578590 588 593 586 Male 2,180 1,927 1,915 1,613 1,624 1,706 1,709 1,791 1,853 1,860 1,886 1,866 Female 2,078 1,833 1,816 1,531 1,543 1,621 1,624 1.703 1,760 1,769 1,795 1,773 Males per 100 females 104.9 105.1 105.5 105.4 105.3 105.3 105.3 105.2 105.3 105.2 105.1 105.2 Age of mother: Under 20 years 594 599 656,595 571 571 554 560 562 537524 499 20-24 years 1,427 1,337 1.419 1,094 1,092 1,146 1,140 1,189 1,226 1,212 1.206 1,160 25-29 years 1,093 926 995 937 972 1,016 1,015 1,069 1,109 1,128 1,152 1,148 30-34 years 688 529 428 376 392 447 474517 550 561 805 625 35-39 years 360 283 180 115 116 121 126 135 141 146 168 180 40 years or more .................... 97 86 53 28 26 26 24 24 24 25 26 27 Birth rate per 1,000 population 23.7 19.4 18.4 14.6 14.6 15.1 15.0 15.6 15.9 15.8 15.9 15.5 White. 22.7 18.3 17.4 13.6 13.6 14.1 14.0 14,5 14.9 14.8 14.9 14.6 Black and other.. 32.1 27.6 25.1 21.0 20.8 21.6 21.6 22.2 22.5 22.0 21.9 21.3 Black 31.927.7 25.3 20.7 20.5 21.4 21.3 22.0 22.1 21.5 21.4 20.9 Male 24.7 20.3 19.4 15.4 15.3 15.9 15.8 16.4 16.8 16,7 16.7 16.4 Female.... 22.8 18.6 17.4 13.8 13.8 14.4 14.2 14.8 15.1 15.0 15.1 14.7 Plural birth ratio? 20.4 20.1 18.1 19.2 19.5 19.2 19,6 19,5 19.3 19.7 19.9 20.3 White....... 19.3 19.0 - 17.3 18.5 18.8 18,5 18,8 18,6 18.5 18.8 19.2 19.6 Black and other 26.3 25.8 21.9 22.1 22.3 22.4 22.9 22.9 22.7 23.0 22.6 22.9 Black... (NA) (NA) - 22.8 23.1 23.3 23.3 24.2 24.2 24.1 24.7 24.1 24.5 Birth rate per 1,000 women 118.0 96.6 87.9 66.0 65.0 66.8 65.5 67.2 68.4 67.4 67.3 65.8 White 113.2) 91.4 | 84.1 62.5 61.5 63.2 61.7 63,4 64.7 63.9 63.962.4 Black and other 153,6 131.9 113.0 87.7 85.8 87.7 87.0 88.5 88.6 86,4 85.5 83.2 Black 153,5 133.2 115.4 87.9 85.888.1 86.7 88.3 88.1 85.4 84.1 81.7 Age of mothor: 10-14 years .6 .8 1.2 1.3 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 15-19 years 89,1 70.5 68.3 56.6 52.8 52.8) 51.5 52.3 53.0 52.7 52.9 51.7 20-24 years 258.1 195.3 167.8 113.0 110.3 112.9 109.9 112.8 115.1 111.8 111,3 108.3 25-29 years 197.4 161.6 145.1 108.2 106.2 111.0 108.5 111.4 112.9 (112.0 111.0 108.7 30-34 years 112.7 | 94.4 73.352.3 53.656.4 57.8 60.3 61.961,464.2 64.6 35-39 years 56.2 46.2 31.7 19.5 19.0 19.219.0 19.5 19,8 20.0 21.1 22.1 40-44 years 15,5 12.8 8.1 4.6 4.3 4.2 3.9 3.9 3.9 3.8 3.9 3.8 45-49 years 5.9 .8 .5 .3 2 2 .2 2 .2 .2 .2 .2 NA Not available. For explanation, see Guide to Tabular Presentation. For 1960, change from 1955. Per 1,000 live births. * 1971. Per 1,000 women, 15-44 years old in specified group. Rate computed by relating births to mothers 45 years old and over to women 45 to 49 years old. Source: U.S. National Center for Health Statistics, Vital Statistics of the United States, annual; and unpublished data. No. 84. BIRTH RATES, BY LIVE-BIRTH ORDER AND RACE: 1960 TO 1983 [Births per 1,000 women 15-44 years old in specified racial group. Live-birth order refers to number of children born alive. Figures for births of order not stated are distributed. See also headnote, table 83, and Historical Statistics, Colonial Times to 1970, series B 20-27) LIVE-BIRTH ORDER ALL RACES WHITE BLACK 1960 1970 1980 1982 1983 1960 1970 1980 1982 1983 1960 1970 1960 1970 1980 1982 1983 Total 118.0 87.9 First birth 31.1 34.2 Second birth 29.2 24.2 Third birth 22.8 13.6 Fourth birth.. 14.6 7.2 Fifth birth 8.3 3.8 Sixth and seventh..... 7.6 Eighth and over......... 4.3 1.8 68.4 67.3 65.8 113.2 84.1 29.5 28.6 27.830.8 32.9 21.8 22.0 21.5 29.2 23.7 10.3 10.2 10.1 22.7 13.3 3.9 3.8 3.7 14.1 6.8 1.5 1.4 1.4 7.5 3.4 1.0 .9 .9 6.1 2.7. .4 .3 3 2.8 1.2 64.7 63.9 62.4 153.5 115.4 28.4 27.7 26.8 33.6 43,3 21.0 21.3 20.8 29.3 27.1 9.5 9,5 9.4 24.0 16.1 3.4 3.3 3.3 18.6 10.0 1.3 1.2 1.2 14.1 6.4 .8 .7 .7 1 18.4 7.0 .3 .3 .2 15.6 5,6 88.1 | 84.1 81.7 35.2 33.0 32.3 25.7 24.9 24.1 14.5 14.2 13.7 6.7 6,5 6.3 3.0 2.8 2.8 2.1 1.9 1.8 .9 .7 .6 3.2 Includes other races not shown separately. Source: U.S. National Center for Health Statistics, Vital Statistics of the United States, annual; and unpublished data