Question

A randomly selected customer is asked if they like hot or iced coffee. Let H be the event that the customer likes hot coffee and let / be the event that the customer likes iced coffee. What is the probability that a randomly selected customer likes hot or iced coffee?

0 0.22
0 0.30
O 0.61
0 0.83

Answer 1

83% or 0.83

Explanation:

The probability that a randomly selected customer likes hot or iced coffee can be found using the formula:

P(H or I) = P(H) + P(I) - P(H and I)

where P(H) is the probability that the customer likes hot coffee, P(I) is the probability that the customer likes iced coffee, and P(H and I) is the probability that the customer likes both hot and iced coffee.

We are given that P(H) = 0.75, P(I) = 0.30, and P(H and I) = 0.22. Therefore:

P(H or I) = 0.75 + 0.30 - 0.22 = 0.83

So the probability that a randomly selected customer likes hot or iced coffee is 0.83, or 83%. This makes sense because some customers may like both hot and iced coffee, and so we cannot simply add the probabilities of liking each type of coffee. By subtracting the probability of liking both, we account for these customers and obtain the correct probability.