Chapter 5.2, Problem 38E

(a)

To determine

Probability replacing the question marks in the table.

Answer to Problem 38E

Question mark in the table should be replaced by 0.218.

Explanation of Solution

Given information:

Assignment of probabilities:

  

Let the missing probability be x .

  

Criteria for valid probability model:

• For each outcome, sum of probabilities should be equal to 1.
• All probabilities should be between 0 and 1 (including both).

Now,

Sum of the probabilities shown in the table needs to be equal to 1.

  $\text{Sum}\text{of}\text{probabilities}=0.040+0.033+0.144+0.234+0.208+x+0.123=1$

Combine all the terms:

  

Subtract 0.782 from both sides:

  $x=0.218$

Thus,

“?” in the table should be replaced by 0.218.

(b)

To determine

Probability for chosen trip did not begin between 9 A.M and 12:59 P.M.

Answer to Problem 38E

Probability,

  $P\left(\text{Not}\text{between}\text{9}\text{A}\text{.M}\text{and}\text{12:59}\text{P}\text{.M}\right)=0.766$

Explanation of Solution

Given information:

Assignment of probabilities:

  

According to complement rule,

  $P\left(A^c\right)=P\left(\text{not}A\right)=1-P\left(A\right)$

  

Note that

Probability of the trip beginning between 9 A.M and 12:59 P.M,

  $P\left(\text{Between}\text{9A}\text{.M}\text{and}\text{12:59}\text{P}\text{.M}\right)=0.234$

Apply complement rule:

  $\begin{array}{l}P\left(\text{Not}\text{between}\text{9}\text{A}\text{.M}\text{and}\text{12:59}\text{P}\text{.M}\right)=1-P\left(\text{Between}\text{9}\text{A}\text{.M}\text{and}\text{12:59}\text{P}\text{.M}\right)\\ =1-0.234\\ =0.766\end{array}$

Thus,

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