62 ELEMENTARY PROBABILITY Ch. 3 



4. If a name is to be selected at random from among those persons who were 

 residents of the United States in 1950 and who then were between the ages of 

 35 and 74, inclusive, estimate the probability that the person so chosen will be 

 aged 50 to 59, inclusive. (See problem 8, section 2.5 for the appropriate table.) 



Ans. .26. 



5. Compute the probability of throwing either a sum of seven or of eleven 

 on one throw of two unbiased dice by enumerating the single events in these two 

 classes of events. Verify your answer by applying the Law of Total Probability. 



6. If five unbiased coins are to be flipped simultaneously, calculate the proba- 

 bility that there will be a 3:2 division of heads and tails, either way. Ans. 5/8. 



7. Verify the probabilities given in the second and tenth lines of Table 3.12 

 by listing all the possible combinations of chromosomes. Where does the matter 

 of single events come into these calculations? 



8. Use the laws of Total and Compound Probabilities to solve problem 7. 



9. Suppose that two bags— identical in appearance — contain, respectively, 20 

 red and 30 blue marbles; and 40 red and 10 blue marbles. If one bag is to be 

 selected at random and then one marble withdrawn from that bag, what is the 

 probability that it will be red? That it will not be red? 



10. If three unbiased dice are to be thrown once, what is the probability that 

 a sum of 4 will be thrown? A sum of at least 4? Ans. 1/72, 215/216. 



11. If the throw described in problem 10 is to be made twice, what is the 

 probability that a sum of 4 will be thrown both times? What is the probability 

 that exactly one sum of 4 will be thrown on the two throws? 



12. Suppose that two babies have been born almost simultaneously in a cer- 

 tain hospital, and that one of the families subsequently claims that the babies 

 were interchanged either willfully or accidentally. The blood classes of the 

 babies and of the parents are as follows: 



Mr. Timofeef is A, MN, P+, and Rh + ; 

 Mrs. Timofeef is B, N, P+, and Rh- ; 



Mr. Brown is B, M, P+, andRh-; 

 Mrs. Brown is O, N, P - , and Rh - . 



The child the Timofeefs now have is O, MN, P-, and Rh + . The child the 

 Browns now have is O, MN, P+, and Rh — . Have the babies been inter- 

 changed? Or is it impossible to tell from this information? Give reasons. 



Ans. No interchange has occurred. 



13. Suppose that a few days after a wealthy man has died a woman claims 

 that a certain girl is her daughter and that the deceased was the father. Also 

 suppose that the following facts about blood classes have been established: 



(1) The deceased's blood was B, M, Rh+, and P+. 



(2) The deceased had a son whose blood was in group O and also was Rh — . 



(3) The alleged mother's blood is A, MN, Rh+, and P+. 



(4) The girl's blood is O, M, Rh-, and P-. 



What conclusions can you draw about the paternity of the girl? Justify your 

 statements with probability evidence based on the following assumptions: (1) 

 For a person whose blood is B it is assumed that the chances are two out of 

 three that the specific type is B/O if no other pertinent information is available 



