In a test for ESP (extrasensory perception), a subject is told that cards the experimenter can see but he 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. The probability that the subject guesses the shape correctly on the first and last card, but incorrectly on the other three cards, is about

a) 0.026.

b) 0.264.

c) 0.090.

Question

Mathematics

Zachery Hayes

6 July, 12:57

In a test for ESP (extrasensory perception), a subject is told that cards the experimenter can see but he 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. The probability that the subject guesses the shape correctly on the first and last card, but incorrectly on the other three cards, is about

a) 0.026.

b) 0.264.

c) 0.090.

+3

Answers (2)

Know the Answer?

Shea Newman · Answer 1

a) 0.026.

Step-by-step explanation:

In order to solve this you just need to mulitply the probability of each of the options that we have, so the first one would be guessing correctly that's a. 25 or 1 out of 4, the second thru 4th would. 75 since that would be guessing anyone but the correct one, and the last one will be. 25 again:

,25*,75*,75*,75*,75*,25=,02636

So the probability of a subject choosing the first one right, and then the second thru fourth wrong and the last one again wrong would be of, 026

Akira Rowe · Answer 2

Akira Rowe 6 July, 16:03

0

0.25 * (1-0.25) ^3*0.25

=0.026