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Chapter 3: Q.55 (page 218)

Use the following information to answer the next four exercises. Table 3.15 shows a random sample of musicians and how they learned to play their instruments

Find P(musician is a male AND had private instruction).

Short Answer

Expert verified

P(musicianisamaleANDhadprivateinstruction)=0.12

Step by step solution

01

Content Introduction

The contingency table shown is below:

02

Content Explanation

It can be seen in the table that total number of musicians is 130,out of these total musicians, 15are male musician who learned music with private instruction. Therefore probability of male musician and a private instructor is as follow:

P(musicianisamaleANDhadprivateinstruction)=TotalmalemusicianswithprivateinstructiontotalmusiciansP(musicianisamaleANDhadprivateinstruction)=15130P(musicianisamaleANDhadprivateinstruction)=0.12

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Most popular questions from this chapter

Suppose a study of speeding violations and drivers who use cell phones produced the following fictional data: Table 3.2.


Speeding violation in the last yearNo speeding violation in the last yearTotal
Uses cell phone while driving25280305
Does not use cell phone while driving45405450
Total70685755

The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and

685. Notice that 305 + 450 = 755 and 70 + 685 = 755.

Calculate the following probabilities using the table.

a. Find P(Driver is a cell phone user).

b. Find P(driver had no violation in the last year).

c. Find P(Driver had no violation in the last year AND was a cell phone user).

d. Find P(Driver is a cell phone user OR driver had no violation in the last year).

e. Find P(Driver is a cell phone user GIVEN driver had a violation in the last year).

f. Find P(Driver had no violation last year GIVEN driver was not a cell phone user)

Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55%prefer life in prison without parole over the death penalty for a person convicted of first degree murder. 37.6%of all Californians are Latino. In this problem, let: 鈥� C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. L = Latino Californians. Suppose that one Californian is randomly selected.

Find P(L).

U and V are mutually exclusive events. P(U) = 0.26; P(V) = 0.37. Find:

a. P(U AND V)

b. P(U|V)

c. P(U OR V)

Use the following information to answer the next two exercises. You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three.

What does P(E OR M) mean in words?

Roll two fair dice separately. Each die has six faces.

a. List the sample space.

b. Let A be the event that either a three or four is rolled first, followed by an even number. Find PA.

c. Let B be the event that the sum of the two rolls is at most seven. Find PB.

d. In words, explain what 鈥�PA|B鈥� represents. Find PA|B.

e. Are A and B mutually exclusive events? Explain your answer in one to three complete sentences, including numerical justification.

f. Are A and B independent events? Explain your answer in one to three complete sentences, including numerical justification.
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