4. A couple plans to have three children. Assume that boys and girls are equally

Question

4. A couple plans to have three children. Assume that boys and girls are equally likely. a) Symbolize the sample space of possible gender combinations. Use a tree diagram to generate the possible simple events b) Let A c) the event that the couple has exactly one girl. Symbolize A, and find P(A). Let B the event that the couple has at least two boys. Symbolize B, and find P(B) d) Let C the event that the couple has exactly one boy. Find P(AUC) 5. Suppose that you have torn a tendon and are facing surgery to repair it. The surgeon explains the following risks to you: infection occurs in 3% of such operations, the repair fails in 14%, and infection and failure occur together in 1%. Use a Venn diagram to illustrate the relationships among these three surgical outcomes. Then, find the percentage of these operations that succeed and are free from infection. herapy (AAMFT) found that 25% of A survey by the American Association for Marriage and Family T divorced couples are classified as fiery foes" who communicate through their children and are hostile to each other. What is the probability that out of a sample of 10 divorced couples, all ten are classified as "fiery foes?" 6.

Explanation / Answer

a)

Sample space, S = { BBB, BBG, BGB, GBB,

BGG, GGB, GBG, GGG }

b)

Event A = { BBG, BGB, GBB }

P(A) = 3C1/8C1 = 3/8

c)

Event B = { BBB, BBG, BGB, GBB }

P(B) = 4C1/8C1 = 4/8 = 0.5

d)

n(A U C) = { BBG, BGB, GBB, BGG, GGB, GBG }

P(A U C) = 6/8 = 0.75

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