Family Planning: Suppose that a couple are planning to have4 children. Suppose t

Question

Family Planning: Suppose that a couple are planning to have4 children. Suppose that the probability that a child will be aboy is about 0.51 and that a child will be of a particular genderindependent of their siblings. We will ignore multiple births since theyare very unlikely. They want 3 girls and 1 boy. (a) Find the probability that they will obtain such a familyand that the boy is the youngest. (b) Find the probability that they will obtain such a family.Hint: The boy can occupy any position. Family Planning: Suppose that a couple are planning to have4 children. Suppose that the probability that a child will be aboy is about 0.51 and that a child will be of a particular genderindependent of their siblings. We will ignore multiple births since theyare very unlikely. They want 3 girls and 1 boy. (a) Find the probability that they will obtain such a familyand that the boy is the youngest. (b) Find the probability that they will obtain such a family.Hint: The boy can occupy any position.

Explanation / Answer

(a) the probability of the first three children being girls is(.49)3=.117649 The probability of the last child (theyoungest) being a boy is .51 .117649*.51=.06000099, or about6% (b) There are 4 ways to have a family of 3 girls and 1boy b g g g g b g g g g b g g g g b The probability of each of these occuringis about 6%, so 6%*4= about 24% (b) There are 4 ways to have a family of 3 girls and 1boy b g g g g b g g g g b g g g g b The probability of each of these occuringis about 6%, so 6%*4= about 24%

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