Question

according to sales records at a local coffee shop, 75% of all customers like hot coffee, 30% like iced coffee, and 22% like both hot and iced coffee. the venn diagram displays the coffee preferences of the customers. 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 the customer likes neither hot nor iced coffee? 0.08 0.17 0.53 0.61

Explanation:

Step1: Calculate the probability of liking hot or iced coffee

The probability of liking hot or iced coffee is the sum of the probabilities of each region in the Venn diagram that is part of either \(H\) or \(I\). So, \(P(H\cup I)=0.53 + 0.22+0.08\).

$$P(H\cup I)=0.83$$

Step2: Calculate the probability of liking neither

The probability of an event \(A\) not occurring is \(P(\overline{A}) = 1 - P(A)\). Let \(A\) be the event of liking hot or iced coffee. Then the probability of liking neither is \(1 - P(H\cup I)\).

$$1 - 0.83=0.17$$

Answer:

0.17