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In a class of 30 students, 18 have a brother and 8 have a sister. There are 9 students who do not have any siblings. What is the probability that a student chosen randomly from the class does not have a brother?
Answer:

In a class of $30$ students, $18$ have a brother and $8$ have a sister. There are $9$ students who do not have any siblings. What is the probability that a student chosen randomly from the class does not have a brother? $\newline$ Answer:

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Probability of independent and dependent events

Full solution

Q. In a class of

30

students,

18

have a brother and

8

have a sister. There are

9

students who do not have any siblings. What is the probability that a student chosen randomly from the class does not have a brother?

\newline

Answer:

Determine Total Students Without Brother: First, we need to determine the total number of students who do not have a brother. We know that there are $18$ students who have a brother and $9$ students who do not have any siblings. Since the total number of students is $30$ , we can find the number of students without a brother by subtracting the number of students with a brother from the total number of students. $\newline$ Calculation: $30$ (total students) - $18$ (students with a brother) = $12$ (students without a brother)
Calculate Probability: Now, we need to calculate the probability that a student chosen randomly from the class does not have a brother. The probability is the number of students without a brother divided by the total number of students. $\newline$ Calculation: Probability = Number of students without a brother / Total number of students = $\frac{12}{30}$
Simplify Fraction: To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is $6$ . $\newline$ Calculation: $\frac{12}{30} = \left(\frac{12}{6}\right) / \left(\frac{30}{6}\right) = \frac{2}{5}$

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