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In a class of 27 students, 13 have a brother and 15 have a sister. There are 11 students who have a brother and a sister. What is the probability that a student who has a brother also has a sister?
Answer:

In a class of $27$ students, $13$ have a brother and $15$ have a sister. There are $11$ students who have a brother and a sister. What is the probability that a student who has a brother also has a sister? $\newline$ Answer:

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Probability of independent and dependent events

Full solution

Q. In a class of

27

students,

13

have a brother and

15

have a sister. There are

11

students who have a brother and a sister. What is the probability that a student who has a brother also has a sister?

\newline

Answer:

Find Students Count: First, we need to find the number of students who have both a brother and a sister. According to the problem, there are $11$ students who have both a brother and a sister.
Determine Students with Brother: Next, we need to determine the number of students who have a brother. The problem states that there are $13$ students who have a brother.
Calculate Probability: Now, we calculate the probability that a student who has a brother also has a sister. This is done by dividing the number of students who have both a brother and a sister by the total number of students who have a brother. $\newline$ Probability = $\frac{\text{Number of students with both a brother and a sister}}{\text{Number of students with a brother}}$ $\newline$ Probability = $\frac{11}{13}$
Simplify Fraction: We simplify the fraction to get the final probability. $\newline$ Probability = $\frac{11}{13}$ $\newline$ This fraction cannot be simplified further, so the probability remains $\frac{11}{13}$ .

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