Question

The marketing department of a nationally known cereal maker plans to conduct a national survey to find out whether or not consumers of flake cereals can distinguish one of their favorite flake cereals. In the survey, eight people were presented with five bowls of flake cereal, and were told that only one contained their favorite. Suppose that the eight persons in the experiment were unable to identify their favorite cereal and just guessed which bowl it was in. What is the probability that none of the eight guessed correctly

Answer 1

Explanation:

The probability that a person answered incorrectly is 4/5

P(1st answered incorrectly AND 2nd answered incorrectly AND

3rd answered incorrectly AND 4th answered incorrectly AND

5th answered incorrectly AND 6th answered incorrectly AND

7th answered incorrectly AND 8th answered incorrectly)

Since "AND" mean to multiply, the probability that none of the 8 guessed correctly is

4/5×4/5×4/5×4/5×4/5×4/5×4/5×4/5

=(4/5)^8

=0.16777216