Question

Customers eat one type of meal. The probabilities of a customer chosen at random eating each type of meal are shown in the table below. 300 customers are chosen at random. How many of these customers would you expect to have eaten chilli?

Pizza = 0.2
Curry =15%
Pasta =3/10
Chilli = ?​

Answer 1

The expected number of customers who ate chilli out of 300 is calculated by finding the missing probability for chilli and then multiplying it by the total number of customers. The probability for chilli is 0.35, so the expected number is 105 customers.

Step-by-step explanation:

The question asks about the expected number of customers who would eat chilli out of 300 customers, given the probability of each type of meal being chosen by a randomly selected customer.

The probabilities for eating pizza, curry, and pasta are provided, but we need to calculate the missing probability for chilli.

To find the probability of a customer eating chilli, we first recognize that the total probability for all meal choices must equal 1 (or 100%). The given probabilities are 0.2 for pizza, 0.15 for curry, and 3/10 (or 0.3) for pasta.

By subtracting these probabilities from 1, we find the probability for eating chilli.

Now, calculate the probability for chilli: 1 - (0.2 + 0.15 + 0.3) = 1 - 0.65 = 0.35.

Therefore, the probability of a customer eating chilli is 0.35 or 35%.

To determine the expected number of customers eating chilli, multiply the total number of customers, 300, by the probability of eating chilli, 0.35.

The expected number is 300 × 0.35 = 105.

Thus, you would expect 105 out of 300 customers to eat chilli.