Question

A psychologist determined that the number of sessions required to obtain the trust of a new patient is 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 propose

X	F(X)
1	.17
2	.33
3	.5

a. Is this probability function valid? Explain.

b. What is the probability that it takes exactly 2 sessions to gain the patient’s trust?

c. What is the probability that it takes at least 2 sessions to gain the patient’s trust?

Answer 1

a) Since, all probabilities are greater than or equal to zero and sum of all probabilities = 0.17 + 0.33 + 0.5 = 1 (equal to 1).

We can say that, this probability function is valid.

b) P(X = 2) = 0.33

Therefore, the probability that it takes exactly 2 sessions to gain the patient’s trust is 0.33

c) P(X ≥ 2) = P(X = 2) + P(X = 3) = 0.33 + 0.5 = 0.83

Therefore, the probability that it takes at least 2 sessions to gain the patient’s trust is 0.83