A psychologist determined that the number of sessions required to obtain the trust of a new patient is either , , or . Let be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed. for or a. Consider the required conditions for a discrete probability function, shown below. Does this probability distribution satisfy equation (5.1)? Yes, all probability function values are greater than or equal to 0 Does this probability distribution satisfy equation (5.2)? Yes, the sum of all probability function values equals 1 b. What is the probability that it takes exactly sessions to gain the patient's trust (to 3 decimals)? 0.333 c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?

The discrete probability relationship for the number of sessions it takes to gain a patient's trust calculated using the information given are :

Yes
Yes
0.333
0.833

x = number of sessions
The number of possible sessions include, 1, 2 or 3

The probability of each number of session could be expressed thus :

Recall ::

P = required outcome / Total possible outcomes

For one session ; x = 1 ;

P(x = 1) = 1 / 6

For 2 sessions., x = 2 ;

P(x = 2) = 2 / 6 = 1/3

For 3 sessions, x = 3 ;

P(x = 3) = 3/6 = 1/2

1.)

Yes, f(x) ≥ 0 is satisfied ; The individual probability values of all possible outcomes must not be less than 0.

2.)

(1/6 + 1/3 + 1/2) = (1 + 2 + 3) / 6 = 6/6 = 1

Yes, Σf(x) = 1 is satisfied ; The sum of the discrete probability of an event must = 1

3.)

Probability that it takes exactly 2 sessions ; x = 2

P(x = 2) = 1/3 = 0.333

4.)

Probability that it takes atleast two sessions : x ≥ 2) :

P(x ≥ 2) = P(x=2) + P(x=3)

P(x ≥ 2) = 0.333 + 0.5 = 0.833

Therefore, the probability that that it takes atleast 2 sessions os 0.833

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