Question

In a test for ESP (extrasensory perception) a subject is told that cards the experimenter can see but the subject cannot contain either a star, a circle, a wave, or a square. As the experimenter looks at each of five cards in turn, the subject names the shape on the card. A subject who is just guessing has probability 0.25 of guessing correctly on each card.

Assume the subject's guesses are independent of each other.

What is the probability that the subject guesses the shape correctly on four out of the five cards? (Enter your answer rounded to four decimal places.)

Answer 1

X ~ bin ( n , p)

Where n = 5 , p = 0.25

Binomial probability distribution is

P(X) = ⁿC_x * p^x * ( 1 - p)^n-x

So,

P(X = 4) = ⁵C₄ * 0.25⁴ * ( 1 - 0.25)

= 0.0146