Question

In a class of students, the following data table summarizes how many students have abrother or a sister. What is the probability that a student has a brother given that theydo not have a sister?

Answer 1

We have to calculate the probability that a student has a brother given that they do not have a sister.

We can find this probability as the quotient between P1, the probability of a student having a brother and no sister, and P2, the probability of a student having no sister.

The total amount of students is 29.

So we can write:

$P(B|noS)=\frac{P(B\cap noS)}{P(noS)}=\frac{\frac{6}{29}}{\frac{6}{29}+\frac{18}{29}}=\frac{6}{6+18}=\frac{6}{24}=0.25$

Answer:

The probability that a student has a brother given that they do not have a sister is P=0.25.