Question

Let x be the number of students who show up for a professor's office hour on a particular day. Suppose that the probability mass function (pmf) of x is p(0) = 0.25, p(1) = 0.30, p(2) = 0.15, p(3) = 0.20, and p(4) = 0.10. What is the probability that at least 2 students show up for the office hour?

1) 0.40
2) 0.45
3) 0.50
4) 0.55

Answer 1

The probability of at least 2 students showing up for the professor's office hour can be calculated by adding the probabilities of 2, 3, and 4 students showing up. The probability that at least 2 students show up for the office hour is 0.45.

Step-by-step explanation:

The probability of at least 2 students showing up for the professor's office hour can be calculated by adding the probabilities of 2, 3, and 4 students showing up.

1. P(x = 2) = 0.15
2. P(x = 3) = 0.20
3. P(x = 4) = 0.10

To find the probability of at least 2 students showing up, we need to find the sum of these probabilities:

P(x ≥ 2) = P(x = 2) + P(x = 3) + P(x = 4) = 0.15 + 0.20 + 0.10 = 0.45

Therefore, the probability that at least 2 students show up for the office hour is 0.45.