A small class has 10 students. Five of the students are male and 5 are female. I write the name of each student on a 3 by 5 card. The cards are shuffled thoroughly and I choose one
at random, observe the name of the student, and replace it in the set. The cards are
thoroughly reshuffled and I again choose a card at random, observe the name, and replace it
in the set. This is done a total of four times. Let X be the number of cards observed in these
four trials with a name corresponding to a male student. The random variable X has which of
the following probability distributions?​

Options are;

A) the Normal distribution, with mean 2 and variance 1

B) the binomial distribution, with parameters n = 4 and p = 0.5

C) the poisson distribution, with parameters λ = 4/10

D) none of the above

B) the binomial distribution, with parameters n = 4 and p = 0.5

Step-by-step explanation:

Number of times card is shuffled is 4 times. Thus; n = 4

X is the number of cards in the time shuffled that corresponds to a male.

We are told there are 10 students and 5 are male and 5 female.

Thus, probability that it corresponds to a male is;

P(corresponding to a male) = 5/10 = 0.5

According to binomial probability distribution, the parameters are;

p = 0.5

n = 4

q = 1 - 0.5 = 0.5

step-by-step :