Question

A family has five children. Assuming that the probability of a girl on each birth was 0.5 and that the five births were independent, what is the probability the family has at least one girl, given that they have at least one boy

Answer 1

Answer:

The probability that the family has at least one girl, given that they have at least one boy 0.80.

Step-by-step explanation:

Construct the sample space for all the 5 children as follows:

S = {GGGGG, GGGGB, GGGBB, GGBBB, GBBBB and BBBBB}

There are a total of 6 outcomes.

First compute the probability of at least 1 boy.

Favorable outcomes : {GGGGB, GGGBB, GGBBB, GBBBB and BBBBB} = 5

Then the probability of at least 1 boy is,

$P(At\ least\ 1\ boy)=\frac{5}{6}$

Of these 5 samples the sample space for at least 1 girl is:

{GGGGB, GGGBB, GGBBB and GBBBB} = 4

Then the probability of at least 1 girl given at least 1 boy is,

$P(At\ least\ 1\ girl|At\ least\ 1\ boy)=\frac{4}{5}=0.80$

Thus, the probability of at least 1 girl given at least 1 boy is, 0.80.