Questions: Following is the probability distribution of a random variable that represents the number of extracurricular activities a college freshman participates in. x 0 1 2 3 4 P(x) 0.04 0.13 0.47 0.22 0.14 (a) Find the probability that a student participates in exactly one activity. The probability that a student participates in exactly one activity is 0.13. (b) Find the probability that a student participates in more than two activities.

Solution Steps

To solve the given problem, we need to find the probability that a student participates in more than two activities. We will sum the probabilities of participating in 3 and 4 activities.

1. Identify the probabilities for participating in 3 and 4 activities from the given distribution.
2. Sum these probabilities to get the total probability of participating in more than two activities.

From the given probability distribution, we have:

• \( P(3) = 0.22 \)
• \( P(4) = 0.14 \)

To find the probability that a student participates in more than two activities, we sum the probabilities of participating in 3 and 4 activities: \[ P(X > 2) = P(3) + P(4) = 0.22 + 0.14 \]

Calculating the sum: \[ P(X > 2) = 0.36 \]

Final Answer