Textbook Problem

A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient’s trust. The following probability function has been proposed.

$f(x)=\frac{x}{6}$      for x = 1, 2, or 3

1. a. Is this probability function valid? Explain.
2. b. What is the probability that it takes exactly 2 sessions to gain the patient’s trust?
3. c. What is the probability that it takes at least 2 sessions to gain the patient’s trust?