20. Suppose a man and woman each carries genes for A and O blood types. As a res

Question

20. Suppose a man and woman each carries genes for A and O blood types. As a result, each of their future children has a 75% chance of having type A blood and a 25% chance of having type O blood. (Type O blood only results if an individual inherits the type O gene from each parent.) Suppose this couple will have 5 children, and let the random variable X represent the number of these children with type O blood. a. Can a binomial distribution be used to describeX If so, check the conditions. What assumptions are you making? b. What is the probability that exactly 2 of the 5 children have type O blood? c. What is the probability that at most 2 of the 5 children have type O blood? How many of the 5 children would you expect to have type O blood? Interpret your answer d.

Explanation / Answer

Ans:

a)Yes,we can use binomial distribution.As there are only two outcomes possible i.e. blood type O(success) or type A (failure) and each trial is independent of each other.

b)Binomial distribution with n=5,p=0.25

P(x=2)=5C2*(0.25)2*(0.75)3=0.2637

using Excel function:

P(x=2)=BINOMDIST(2,5,0.25, FALSE)=0.2637

c)P(x<=2)=5C0*(0.25)0*(0.75)5+5C1*(0.25)1*(0.75)4+5C2*(0.25)2*(0.75)3

=0.2373+0.3955+0.2637

=0.8965

using Excel function:

P(x<=2)=BINOMDIST(2,5,0.25, TRUE)=0.8965

d)Expected number of children having blood type O= np=5*0.25=1.25

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