Question

30% of students in the class girls. find the probability that randomly selected group of 5 students include 3 girls.

Answer 1

Answer:

The probability that there are 3 girls in the group of 5 is 0.1323.

Step-by-step explanation:

Let X = number of girls.

The probability of selecting a girl is, p = 0.30.

The sample of students selected is of size, n = 5.

The random variable X follows a Binomial distribution with parameter n and p.

The probability mass function of a Binomial distribution is:

$P(X=x)={5\choose x}0.30^{x}(1-0.30})^{5-x};\ x=0,1,2....$

Compute the probability that there are 3 girls in the group of 5 as follows:

$P(X=3)={5\choose 3}0.30^{3}(1-0.30})^{5-3}\\=10\times 0.027\times 0.49\\=0.1323$

Thus, the probability that there are 3 girls in the group of 5 is 0.1323.