Question

Can someone please help me ??

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 1

The probability of a student having a brother given that they have a sister can be calculated using conditional probability.

Let
`\(A\)` be the event of having a brother, and
`\(B\)` be the event of having a sister.

From the information provided:

-
`\(P(A) = (5)/(24)\)` (5 out of 24 students have a brother)

-
`\(P(B) = (16)/(24)\)` (16 out of 24 students have a sister)

-
`\(P(A \cap B)\) = \(P(A)\)`(since having a brother and having a sister are independent events, there's no direct information about this overlap)

The conditional probability formula is:
`\(P(A|B) = (P(A \cap B))/(P(B))\)`

Substituting the known values:

`\[P(A|B)` =
`(P(A))/(P(B)) = ((5)/(24))/((16)/(24)) = (5)/(16)\]`

Therefore, the probability that a student has a brother given that they have a sister is
`\((5)/(16)\).`

Explanation: