Question

Male children. While it is often assumed that the probabilities of having a boy or a girl are the same, the actual probability of having a boy is slightly higher at 0.51. Suppose a couple plans to have 3 kids. A) Use the binomial model to calculate the probability that two of them will be boys. B) Write out all possible orderings of 3 children, 2 of whom are boys. Use these scenarios to calculate the same probability from part (a) but using the addition rule for disjoint outcomes. Confirm that your answers from parts (a) and (b) match. C) If we wanted to calculate the probability that a couple who plans to have 8 kids will have 3 boys, briefly describe why the approach from part (b) would be more tedious than the approach from part (a). 1) (32)0.512 ∗ 0.49 = 0.3822) BBG,BGB,GBB,GGB,GBG,BGG,GGG,BBBP(2boy) = BBG + GBB + BGBBBG + BGB + GBB + GGB + GBG + BGG + GGG + BBB = 3/8 = 0.375So since boy and girl has slight different probablity, two answer will be different but they are close3) Because using approach, you will have to list all 56 combinations

Answer 1

Answer:

Step-by-step explanation:

Since the actual probability of having a boy child is 0.51, the probability of having a girl child will be (1 - 0.51) = 0.49

A couple plans to have 3 kids; 2 of whom are boys

(A) Using the binomial model, the probability that 2 of the 3 children will be boys is (2/3) × 0.51 = 0.34

(B) The possible orderings of the 3 children are given below:

B1 B2 G / B1 G B2

B2 B1 G / B2 G B1

G B1 B2 / G B2 B1

Where B1 is one male child and B2 is the other male child

(C)  If we wanted to calculate the probability that a couple who plans to have 8 kids will have 3 boys, briefly describe why the approach from part (b) would be more tedious than the approach from part (a)

If the probability of 2/3 is 0.34 then the probability of 3/8 will be 0.1912 when you cross multiply