Question

The Eco Pulse survey from the marketing communications firm Shelton Group asked individuals to indicate things they do that make them feel guilty (Los Angeles Times, August 15, 2012). Based on the survey results, there is a 0.39 probability that a randomly selected person will feel guilty about wasting food and a 0.27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room. Moreover, there is a 0.12 probability that a randomly selected person will feel guilty for both of these reasons.

Required:
a. What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both (to 2 decimals)?
b. What is the probability that a randomly selected person will not feel guilty for either of these reasons (to 2 decimals)?

Answer 1

a) 0.54 = 54% probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both.

b) 0.46 = 46% probability that a randomly selected person will not feel guilty for either of these reasons

Explanation:

We use Venn's Equations for probabilities.

I am going to say that:

P(A) is the probability that a randomly selected person will feel guilty about wasting food.

P(B) is the probability that a randomly selected person will feel guilty about leaving lights on when not in a room.

0.12 probability that a randomly selected person will feel guilty for both of these reasons.

This means that
`P(A \cap B) = 0.12`

0.27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room.

This means that
`P(B) = 0.27`

0.39 probability that a randomly selected person will feel guilty about wasting food

This means that
`P(A) = 0.39`

a. What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both (to 2 decimals)?

`P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.39 + 0.27 - 0.12 = 0.54`

0.54 = 54% probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both.

b. What is the probability that a randomly selected person will not feel guilty for either of these reasons (to 2 decimals)?

`p = 1 - P(A \cup B) = 1 - 0.54 = 0.46`

0.46 = 46% probability that a randomly selected person will not feel guilty for either of these reasons