Question

question
in a class of 24 students, 5 have a brother and 16 have a sister. there are 5 students who do not have any siblings. what is the probability that a student has a brother given that they have a sister?
answer attempt 1 out of 2

Explanation:

Step1: Find number of students with sister and brother

Total students = 24, students with no siblings = 5. So students with siblings = \(24 - 5 = 19\). Students with brother = 5, students with sister = 16. Let \(A\) be having a brother, \(B\) be having a sister. We know \(n(A \cup B)=19\), \(n(A)=5\), \(n(B)=16\). Using \(n(A \cup B)=n(A)+n(B)-n(A \cap B)\), so \(19 = 5 + 16 - n(A \cap B)\), thus \(n(A \cap B)=2\).

Step2: Calculate conditional probability

Conditional probability \(P(A|B)=\frac{P(A \cap B)}{P(B)}=\frac{n(A \cap B)}{n(B)}\). \(n(A \cap B)=2\), \(n(B)=16\). So \(P(A|B)=\frac{2}{16}=\frac{1}{8}\).

Answer:

\(\frac{1}{8}\)