Question

At a school prom, 75% of students show up with a date and 30% arrive in a limo. These events are independent. A journalism student will randomly select 4 students to interview. What is the probability the first three students will be with dates and the fourth will have arrived in a limo?

Answer 1

This is a probability question involving independent events. Independent events are events that do not affect each other's probability of occurrence. The probability of two independent events occurring together is equal to the product of their individual probabilities.

Let D be the event that a student shows up with a date, and L be the event that a student arrives in a limo. We are given that P(D) = 0.75 and P(L) = 0.3, and that these events are independent. We want to find the probability that the first three students are with dates and the fourth student arrived in a limo, or P(DDDL).

Since the events are independent, we can use the rule of product to multiply the probabilities:

P(DDDL) = P(D) times P(D) times P(D) times P(L)

$$P(DDDL) = 0.75 times 0.75 times 0.75 times 0.3

P(DDDL) = 0​.1265625

Therefore, the probability that the first three students will be with dates and the fourth will have arrived in a limo is 0​.1265625, or about 12.65625%