A check of dorm rooms on a large college campus revealed that 27.5% had refriger

Question

A check of dorm rooms on a large college campus revealed that 27.5% had refrigerators, 32.5% had TVs, and 10% had both a TV and a refrigerator.
[Answer all questions below to 3 decomal places. The answers must be given as a fraction, not percentage. For instance, if the answer is 20.7% , it must be typed as 0.207.]

What is the probability that a randomly selected dorm room has "a TV or a refrigerator"? Answer to three decimal places.

What is the probability that a randomly selected dorm room has "a TV or a refrigerator, but not both"? Answer to three decimal places.

What is the probability that a randomly selected dorm room has "neither TV nor refrigerator"? Answer to three decimal places.

Explanation / Answer

Prob. of Only refrigerator = 0.275 - 0.1 = 0.175
Prob of only tv = 0.325 - 0.1 = 0.225
Prob of both tv and refrigerator = 0.1

a) P(either a tv or a refrigerator) = 0.175+0.225+0.1 = 0.500

b) P(tv or a refrigerator but not both) = 0.175+0.225 = 0.400

c) P(neither tv nor refrigerator) = 1 - P(either a tv or a refrigerator) = 1- 0.5 = 0.500

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