Suppose that a particular trait (such as eye color or left handedness) of a pers

Question

Suppose that a particular trait (such as eye color or left handedness) of a person is classified on the basis of one pair of genes and suppose that D represents a donimant gene and R represents a recessive gene. A person with DD genes is pure dominance, one with RR is pure recessive and one with RD (or DR) is hybrid. The pure dominance and hybrid are alike in appearance. Children recieve one gene from each parent. If, with respect to a particular trait, two hybrid parents have a total of 4 children, what is the probability that 3 of 4 children have outward appearance of the dominant gene?

Explanation / Answer

I'm going to assume that is want the Probability that ONLY 3 of the 4 have the trait and not the probability that AT LEAST 3 have the trait. When two hybrid parents make a baby: P(DD)=1/4 P(DR)=2/4 P(RR)=1/4 and a success is defined as either DD or DR (because hybrid children will express the dominant gene) P(DD or DR)=3/4 the Probability of having EXACTLY three successes in 4 trials is equal to: (4 choose 3)*(1/4)*(3/4)^3 = 4*(1/4)*(1/(4^3)) =4*(1/(4^4)) =1/(4^3) =1/64

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