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Chapter 6: Q.10 (page 410)

A test for extrasensory perception (ESP) involves asking a person to tell which of 5shapes鈥攁 circle, star, triangle, diamond, or heart鈥攁ppears on a hidden computer screen. On each trial, the computer is equally likely to select any of the 5shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first 4shapes incorrectly but gets the fifth correct?

a). 1/5

b). 454

c). 45415

d). 5145415

e).4/5

Short Answer

Expert verified

A correct answer is an option (c)45415.

Step by step solution

01

Given Information 

A test for extrasensory perception (ESP) involves asking a person to tell which of 5shapes鈥攁 circle, star, triangle, diamond, or heart鈥攁ppears on a hidden computer screen.

02

Explanation 

The number of positive outcomes divided by the total number of possible outcomes equals the probability:

p=P(win)=#of favorable outcomes#of possible outcomes=15

Because the variable represents the number of tries required before a success, the distribution is geometric.

Geometric probability is defined as follows:

P(X=k)=qk-1p=(1-p)k-1p

Evaluate at k=5:

P(X=5)=1-155-115=45415

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