Question

Suppose a "psychic" is being tested to determine if she is really psychic. A person in another room concentrates on one of five colored cards, and the psychic is asked to identify the color. Assume that the person is not psychic and is guessing on each trial. Define a success as "psychic identifies correct color". (a) What is p, the probability of success on a single trial? (show 1 decimal place) (b) If we conduct 10 trials, what is the probability that the psychic guesses zero or one of the colors correctly? (show 2 decimal places) (c) What is the mean or expected value of X, the number of correct answers out of 10 trials?

Answer 1

there are 5 possible color cards and one of them is correct.

The success for the psychic is guessing the correct color.

a) the probability of success on a single trial is same as the probability that psychic identifies correct color

ans: the probability of success on a single trial is p=0.2

b) Let X be the number of times the psychic guesses the colors correctly out of 10 trials.

We can say that X has a Binomial distribution with parameters, number of trials n=10 and success probability p=0.20

The Binomial probability that X=x times the psychic guesses the colors correctly is

the probability that the psychic guesses zero or one of the colors correctly is

ans: the probability that the psychic guesses zero or one of the colors correctly is 0.38

c) The expected value of X (using the formula for Binomial expectation) is

ans: the mean or expected value of X, the number of correct answers out of 10 trials is 2