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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—a circle, star, triangle, diamond, or heart—appears 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—a circle, star, triangle, diamond, or heart—appears 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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Most popular questions from this chapter

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

Define T=X+Y.

Find and interpret μT.

How well does it fit? (3.2) Discuss what s, r2, and the residual plot tells you about this linear regression model.

Refer to the previous Check Your Understanding (page 390 ) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined X=the number of Patti's correct guesses.

1. Find μX. Interpret this value in context.

2. Find localid="1649452775386" σX. Interpret this value in context.

76. Rhubarb Suppose you purchase a bundle of 10bare-root rhubarb plants. The sales clerk tells you that on average you can expect 5%of the plants to die before producing any rhubarb. Assume that the bundle is a random sample of plants. Let Y= the number of plants that die before producing any rhubarb. Use the binomial probability formula to find
P(Y=1). Interpret this result in context.

79. Sowing seeds Refer to Exercise 69.

(a) Find the probability that exactly17 seeds germinate. Show your work.
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