In a test for extrasensory perception, the experimenter looks at cards containing either a star, circle, wave, or square. (The subject cannot see the cards.) As the experimenter looks at each of 20 cards, the subject names the shape on the card. Assuming that any success guessing shapes is due purely to chance, what is the probability a subject correctly guesses at least 10 of the 20 shapes? (Round to 3 decimal places)

Answer:0.0139Step-by-step explanation:Given that in a test for extrasensory perception, the experimenter looks at cards containing either a star, circle, wave, or square. (The subject cannot see the cards.) Probability for guessing a correct shape out of 4 shapes = 0.25Each trial is independent of the otherHence X no of correct guesses is binomial with n = number of cards = 20 and p = constant probability =0.25 the probability a subject correctly guesses at least 10 of the 20 shapes=[tex]P(X\geq 10)\\= 1-F(9)[/tex], where F represents the cumulative probability upto 9= 0.0139