122 Probability 



QUESTIONS AND PROBLEMS 



1. If a family contains six children, what is the probability that all 

 will be boys; that all will be girls; that there will be four boys and two 

 girls ? 



2. If a penny, dime, and nickel are tossed at the same time, what is 

 the chance that there will be three heads; that there will be two heads 

 and a tail; that the penny and dime will be heads and the nickel tail? 



3. A man tosses a penny 200 times and gets 150 heads and 50 tails. 

 Using x^, figure the probability of this result. Can the deviation be 

 attributed to chance? If not, how could you account for it? 



4. In drawing blindly from a complete pack of cards which has been 

 thoroughly shuffled, what is the chance of drawing a red ace; the ace of 

 diamonds; a red card? 



5. A man draws the ace of diamonds from a pack of cards. What is 

 the chance that he will draw the ace of hearts on the next draw ? Is the 

 chance any different whether or not he replaces the ace of diamonds be- 

 fore he makes the second draw ? Why ? 



6. What is the chance that one of the four hands in a bridge game 

 will contain all spades? 



7. Two men draw seven cards each from a complete pack, replacing 

 each card and reshuffling after each draw. A draws one heart, three 

 diamonds, two spades, and a club. B draws six hearts and a club. 

 What is the chance that A will draw a heart on the eighth draw ? What 

 is the chance that B will draw a heart on the eighth draw? 



8. Family A has four boys and family B four girls. Which family 

 has a better chance of obtaining a boy for the fifth child? Explain. 



9. In maize, green silks are dominant to salmon. Maize is regularly 

 cross-pollinated. A farmer who had both varieties sows the seeds of a 

 plant which was heterozygous (Smsm), but he has no idea of the male 

 parentage of these seeds. He obtains 74 green-silked and 39 salmon- 

 silked plants. Using x^, figure the probability that this is a 1 : 1 and 

 that it is a 3 : 1 ratio. From the probabilities obtained, what would you 

 conclude as to the male parent or parents of these seeds? 



10. A farmer has one green-silked maize plant growing in a field of 

 salmon-silked plants. He detassels the green-silked plant. He uses the 

 seed from this plant and obtains 167 green-silked and 173 salmon-silked 

 plants in the next generation. What is the probability that this plant 

 was a heterozygote ? What is the possibility that it was a homozygote? 



11. A heterozygote, when selfed, gives 632 dominants and 199 reces- 

 sives. What is the probabihty that this is a 3 : 1 ratio? Figure this by 

 both the standard error and x^ methods and compare the results. Are 

 they identical? Are they fundamentafly different or is the difference 

 between the two methods insignificant? 



