Question

Assume that girls and boys are equally likely and the event "having a girl" does not affect the future/past probability of "having a boy" and vice versa. Also, there are no twins. You see a woman walking on the street with a girl. She tells you that she has three children and that the girl with her is her daughter. a) What is the probability that she has two boys? Incorrect: Your answer is incorrect. (enter a fraction) b) What is the probability that she has at least one boy? (enter a fraction)

Answer 1

Soln,

Given that having a girl or having a boy child is equally likely and also there are no twins hence Probability of having a boy P(Boy)=1/2=0.5

Also P(Girl)=0.5 and also the women has 3 childern that means n=3

a)Now according to question

Out of three childerenwhat is the Probability that she has 2 boys. Can be calculated

Let X=2 ; no of boys.

So, P( 2boys and 1 girls)=_nC_c × P(boy)^x ×P(boy)^n-x

P(2 boys 1 girl)= 3×(0.5)²×(0.5)= 0.375

Also,

b) Probability of at least 1 boy can also be said that 1- proprobaility of having no boy

that is P(at least on boy)=1- P(all girls)

probaility of all girls ;P(all girls) = 0.5³= 0.125

hence P(at least on boy)=1-0.125= 0.875