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. To test the questionnaire and procedure to be used, eight persons were asked to cooperate in an experiment. Five very small bowls of flake cereals were placed in front of a person. The bowls were labeled A, B, C, D and E. The person was informed that only one bowl contained his or her favorite flake cereal. 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

0.167772

Explanation:

Given that eight persons were asked to cooperate in an experiment. Five very small bowls of flake cereals were placed in front of a person

Since each one makes only guess probability for correct guess is

=
`(1)/(5) =0.20`

Each person is independent of the other

Hence X no of persons out of eight persons selected to guess correctly is binomial with n =8 and p = 0.2

Required probability

=the probability that none of the eight guessed correctly

=
`P(X=0)\\=(1-0.2)^8\\=0.167772`