Question

Pepsi Tm or Coke Tm ? An experiment is conducted at a local supermarket, where shoppers are asked to taste two soft-drink samples-one Pepsi and one Coke-and state their preference. Suppose that four shoppers are chosen at random and asked to participate in the experiment and that there is actually no difference in the taste of the two brands. a. What is the probability that all four shoppers choose Pepsi? b. What is the probability that exactly one of the four shoppers chooses Pepsi?

Answer 1

The probability that all four shoppers choose Pepsi is 1/16. The probability that exactly one of the four shoppers chooses Pepsi is 1/16.

Step-by-step explanation:

To find the probability that all four shoppers choose Pepsi, we need to consider that there is actually no difference in the taste of the two brands. Since there are only two options (Pepsi or Coke) and each shopper chooses at random, the probability that any single shopper chooses Pepsi is 1/2. To find the probability that all four shoppers choose Pepsi, we multiply the probabilities together: (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

To find the probability that exactly one of the four shoppers chooses Pepsi, we again consider that each shopper chooses at random. The first shopper has a 1/2 chance of choosing Pepsi, and the remaining three shoppers have a 1/2 chance of choosing Coke. We can calculate this probability by multiplying the probabilities together: (1/2) * (1/2) * (1/2) * (1/2) = 1/16.