Chapter 7.2, Problem 7.33E

(a)

To determine

To Calculate: the probability for $\text{P}\left(\text{C}\right)\text{and}\text{P}\left(\text{D}\right)$ .

Answer to Problem 7.33E

0.75

Explanation of Solution

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

For the not happening event is subtracted by happening event from the one.

  $\begin{array}{c}\text{P}\left(\text{C}\right)\text{=1-P}\left(\text{face}\right)\\ \text{=1-}\frac{\text{12}}{\text{52}}\\ \text{=}\frac{\text{10}}{\text{13}}\\ \text{=0}\text{.77}\end{array}$

  $\begin{array}{c}\text{P}\left(\text{D}\right)\text{=1-P}\left(\text{hearts}\right)\\ \text{=1-}\frac{\text{13}}{\text{52}}\\ =\frac{39}{52}\\ \text{=}\frac{\text{3}}{\text{4}}\\ \text{=0}\text{.75}\end{array}$

(b)

To determine

To Explain: the event “C and D” and calculate the $\text{P}\left(\text{C}\text{and D}\right)$ .

Answer to Problem 7.33E

0.58

Explanation of Solution

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

C and D means is the event of a card that is not a face card AND is a club, spade or diamond.

Total sample space = 52

Favourable outcomes = 30

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ =\frac{30}{52}\\ =0.58\end{array}$

(c)

To determine

To Explain: the event “C or D” and calculate the $\text{P}\left(\text{C}\text{or D}\right)$ .

Answer to Problem 7.33E

0.94

Explanation of Solution

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

C or D means is the event of a card that is not a face card OR is a club, spade or diamond.

Total sample space = 52

Favourable outcomes = 49

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ =\frac{49}{52}\\ =0.94\end{array}$