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Chapter 5: Q. 38 (page 327)

When did you leave? The National Household Travel Survey gathers data on the time of day when people begin a trip in their car or other vehicle. Choose a trip at random and record the time at which the trip started. Here is an assignment of probabilities for the outcomes :

a. What probability should replace 鈥�?鈥� in the table? Why?

b. Find the probability that the chosen trip did not begin between 9A.M. and 12:59P.M.

Short Answer

Expert verified

Part(a) 0.218 is the probability that should replace "?" in the table.

Part(b) 0.766 is the probability that the chosen trip did not begin between 9 A.M. and 12:59 P.M.

Step by step solution

01

Part(a) Step 1 : Given information

We need to find the missing probability in given table.

Time of day
10P.M-12.59A.M
1A.M-5.59A.M
6A.M-8.59A.M
9A.M-12.59P.M
Probability
0.040
0.033
0.144
data-custom-editor="chemistry" 0.234
Time of day
1P.M-3.59P.M
4P.M-6.59P.M
7P.M-9.59P.M
Probability
0.208
?
0.123
02

Part(a) Step 2 : Simplify

As we know, Sum of all probabilities should be 1and probability should lie between 0and 1.

Now,

Sum of probabilities is 0.040+0.33+0.144+0.234+0.208+?+0.123=1

Missing probability is 1-0.782=0.218

Hence, 0.218 should replace 鈥�?鈥� in the table.

03

Part(b) Step 1 : Given information

We need to find probability that the chosen trip did not begin between 9 A.M. and 12:59 P.M.

04

Part(b) Step 2 : Simplify

Using complement rule,

P(Ac)=P(1-A)

It is given that P( Between 9A.M and 12:59P.M) is 0.234

Now,

P( Not Between 9A.M and 12:59 P.M) =1-0.234=0.766

Hence, 0.766is the probability that the chosen trip did not begin between 9A.M and 12:59 P.M .

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