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Question

The mad scientist, Tanya has created a pill that a woman can take to increase the likelihood of having a girl baby to twice that of having a boy. If a woman takes the pill consistently what are the chances that, out of five children, there are at least 2 girls? What is the expected number of girls in 5 children?

Answer 1

P(G) = 2/3  

 

Expected number of girls in 5 children = P(G)*5 = 10/3 ~ 3.33

 

P(at least 2 girls) = 1 - [P(0 girls) + P(1 girl)]  

 

P(0 girls) = (1/3)⁵ = 1/243

 

P(1 girl) = ₅C₁ * (2/3)¹ * (1/3)⁴ 

             = 5 * (2/3) * (1/81) = 10/243

 

So P(at least 2 girls) = 1 - [1/243 + 10/243] = 1 - 11/243 = 232/243 ~ 0.9547 ~ 95.47%