among customers- 70% buy popcorn, 40% buy ice cream, and 25% by both. Suppose you pick one customer at random. Find the probability the customer buys popcorn or ice cream.
To find the probability that a customer buys popcorn or ice cream, we need to add the probabilities of buying popcorn and buying ice cream and then subtract the probability of buying both since we don't want to double count those customers.
Let's break down the given information:
- 70% of customers buy popcorn.
- 40% of customers buy ice cream.
- 25% of customers buy both popcorn and ice cream.
To find the probability of buying popcorn or ice cream, we can use the principle of inclusion-exclusion. This states that the probability of the union of two events (A or B) is equal to the sum of their individual probabilities minus the probability of their intersection (A and B).
The probability of buying popcorn or ice cream is calculated as follows:
P(popcorn or ice cream) = P(popcorn) + P(ice cream) - P(popcorn and ice cream)
Let's substitute the given values into the equation:
P(popcorn or ice cream) = 70% + 40% - 25%
Calculating this:
P(popcorn or ice cream) = 70% + 40% - 25%
P(popcorn or ice cream) = 110% - 25%
P(popcorn or ice cream) = 85%
Therefore, the probability that a randomly picked customer buys popcorn or ice cream is 85%.