Question

Suppose a restaurant offers three different types of desserts: cake, pie, and ice cream. The probability that a customer orders cake is 0.4, the probability that a customer orders pie is 0.3, and the probability that a customer orders ice cream is 0.3. Suppose three random customers are ordering desserts, what is the probability that at least one of them orders an ice cream?

Answer 1

The probability that at least one of three customers orders ice cream is approximately 0.657 or 65.7%, calculated using the complement rule and the individual probabilities for each dessert option.

Step-by-step explanation:

The question revolves around calculating the probability that at least one of three customers orders ice cream, given the probabilities of each dessert option. To determine this, we'll use the complement rule. The complement rule suggests that the probability of at least one event happening is equal to 1 minus the probability of none of the events happening (the complement). In this case, we're interested in finding 1 minus the probability that no customer orders ice cream. If the probability of ordering ice cream is 0.3 for each customer, then the probability that a customer does not order ice cream is 1 - 0.3 = 0.7. Since the customers are independent, we calculate this for all three customers.

The probability that no customers order ice cream is (0.7)^3. Therefore, the probability that at least one customer orders ice cream is 1 - (0.7)^3.

Calculating this, we get: 1 - 0.343 = 0.657

So, the probability that at least one of three customers orders ice cream is approximately 0.657 or 65.7%.