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 “?” in the table? Why?
b. Find the probability that the chosen trip did not begin between $9$ A.M. and $12 : 59$ P.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

Part(a) Step 1 : Given information

We need to find the missing probability in given table.

Time of day	$10 P . M - 12.59 A . M$	$1 A . M - 5.59 A . M$	$6 A . M - 8.59 A . M$	$9 A . M - 12.59 P . M$
Probability	$0.040$	$0.033$	$0.144$	data-custom-editor="chemistry" $0.234$

Time of day	$1 P . M - 3.59 P . M$	$4 P . M - 6.59 P . M$	$7 P . M - 9.59 P . M$
Probability	$0.208$	?	$0.123$

Part(a) Step 2 : Simplify

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

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 “?” in the table.

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.

Part(b) Step 2 : Simplify

Using complement rule,

$P (A^{c}) = P (1 - A)$

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

Now,

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

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

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Exercise	Sedan	SUV	Truck
Yes	$25$	$15$	$12$
No	$20$	$24$	$24$

Short Answer

Step by step solution

Part(a) Step 1 : Given information

Part(a) Step 2 : Simplify

Part(b) Step 1 : Given information

Part(b) Step 2 : Simplify

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