Question

In a class of 30 students, a sample of three students are randomly late for class.

The probability that exactly one of the latecomers is a girl is three-fourths the probability that exactly one of the latecomers is a boy.

Calculate the proportion of boys in the class.

Answer 1

In a class of 30 students, a sample of 3 students are randomly late for class.

Let, the proportion of boys in the class is p.

Then, the proportion of girls in the class is 1-p.

Now, this means that a randomly selected student from the class is a boy is with probability p; and the probability that a randomly selected student is girl is 1-p.

Now, if of the 3 latecomers, X is the number of boys in the class, and Y is the number of girls in the class,

then

X follows binomial with parameter n=3 and p.

Y follows binomial with parameter n=3 and 1-p.

Now, it is given that, probability that exactly one latecomer is a girl, is three fourths the probability that exactly one of the latecomers is a boy.

So, we note

So, we can say, that the proportion of boys in the class is 3/7.