Question

Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that 4% of respondents did not provide a response, 26% said that their experience fell short of expectations, 65% of the respondents said that their experience met expectations (Clarkson Magazine, Summer, 2001). If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations? If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?

Answer 1

Answer:

(a) The probability that a randomly selected alumnus would say their experience surpassed expectations is 0.05.

(b) The probability that a randomly selected alumnus would say their experience met or surpassed expectations is 0.67.

Step-by-step explanation:

Let's denote the events as follows:

A = Fell short of expectations

B = Met expectations

C = Surpassed expectations

N = no response

Given:

P (N) = 0.04

P (A) = 0.26

P (B) = 0.65

(a)

Compute the probability that a randomly selected alumnus would say their experience surpassed expectations as follows:

$P(C) = 1 - [P(A) + P(B) + P(N)]\\= 1 - [0.26 + 0.65 + 0.04]\\= 1 - 0.95\\= 0.05$

Thus, the probability that a randomly selected alumnus would say their experience surpassed expectations is 0.05.

(b)

The response of all individuals are independent.

Compute the probability that a randomly selected alumnus would say their experience met or surpassed expectations as follows:

$P(B\cup C) = P(B)+P(C)-P(B\cap C)\\=P(B)+P(C)-P(B)\times P(C)\\= 0.65 + 0.05 - (0.65\times0.05)\\=0.6675\\\approx0.67$

Thus, the probability that a randomly selected alumnus would say their experience met or surpassed expectations is 0.67.