A family has five kids. Assume that each child has an equal chance of being...

Talamancoeb

Talamancoeb

Answered

2021-12-16

A family has five kids. Assume that each child has an equal chance of being a male or a girl. Find the probability that the family has 5 girls if it is known the family has at least one girl.

Answer & Explanation

ol3i4c5s4hr

ol3i4c5s4hr

Expert

2021-12-17Added 48 answers

Step 1
Given that the family has 5 children.
Assume that each child is as likely to be a boy as it is to be a girl.
That is, P(girl)=P(boy)=12.
Consider,
P(5girls|at least one girl)=P5girls and at least one girlP(at least one girl)
=P5girlsP(at least one girl) (1)
Step 2
Let us define the random variable X as the number of girls follows Binomial distribution with n=5 and probability of girl child is p=12.
P(X=x)=(5Cx)(12)x(112)5x=(5Cx)(12)x(12)5x.
P(X=5)=(5C5)(12)5(12)55=0.03125 (2)
P(X1)=1P(X<1)=1P(X=0)=1(5C0)(12)0(12)50=10.03125=0.96875 (3)
Substitute (2) and (3) in equation (1)
P(5girls|at least one girl)=P5girlsP(at least one girl)
=0.031250.96875
=0.032258
raefx88y

raefx88y

Expert

2021-12-18Added 26 answers

Step 1 
A family has five kids. Assume that each child has an equal chance of being a boy or a girl. If it is known that the family has at least one girl, calculate the likelihood that there are 5 girls.
So, there are 
2×2×2×2×2 (2 raised to the 5th power) 
=32 sequences of 5 children. 
As we already know that only one of them is all female, the probability of five female births in a row when all births are independent and 
p(B)=p(G)=0.5 is p(G,G,G,G,G)=132=0.03125 
Note, that this comes out to be the same as simply multiplying the probability of a girl five times because there is only one of these sequences. if you wanted to know the probability of 2 girls and 3 boys, you have to know how many sequences have 2 girls and 3 boys and adjust accordingly.

nick1337

nick1337

Expert

2021-12-28Added 573 answers

You have a 5050 chance of it becoming an a boy or a girl.
The chance the first is a girl is 50%. The chance the second is also 50%, and so on.
Therefore the chance that all five are girls is (0.5)2 or 3.125%

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