Chapter 11.8, Problem 7E

1.

To determine

To determine whether the events are disjoint or overlapping.

Answer to Problem 7E

The events are disjoint.

Explanation of Solution

Given information:

The given statement is:

“A bag contains $3$ red marbles, $4$ black marbles, $4$ blue marbles and $3$ yellow marbles. You randomly draw a marble from the bag. What is the probability that you draw a red or a blue marble?”

The events are disjoint because both a red and a blue marble cannot be drawn at the same time.

2.

To determine

To determine the probability of drawing a red marble.

Answer to Problem 7E

Hence, the probability of drawing a red marble is $\text{P}\left(\text{A}\right)\text{=}\frac{3}{14}$ .

Explanation of Solution

Given information:

The given statement is:

“A bag contains $3$ red marbles, $4$ black marbles, $4$ blue marbles and $3$ yellow marbles. You randomly draw a marble from the bag.”

Calculation:

The probability of drawing a red marble is:

  $\begin{array}{l}\text{Total number of possible outcomes}=3+4+4+3=14\\ \text{Number of events of drawing a red marble}=3\\ \text{Probability of drawing a red marble P}\left(\text{A}\right)\text{=}\frac{3}{14}\end{array}$

Hence, the probability of drawing a red marble is $\text{P}\left(\text{A}\right)\text{=}\frac{3}{14}$ .

3.

To determine

To determine the probability of drawing a blue marble.

Answer to Problem 7E

Hence, the probability of drawing a blue marble is $\text{P}\left(\text{B}\right)\text{=}\frac{2}{7}$ .

Explanation of Solution

Given information:

The given statement is:

“A bag contains $3$ red marbles, $4$ black marbles, $4$ blue marbles and $3$ yellow marbles. You randomly draw a marble from the bag.”

Calculation:

The probability of drawing a blue marble is:

  $\begin{array}{l}\text{Total number of possible outcomes}=3+4+4+3=14\\ \text{Number of events of drawing a blue marble}=4\\ \text{Probability of drawing a blue marble P}\left(\text{B}\right)\text{=}\frac{4}{14}=\frac{2}{7}\end{array}$

Hence, the probability of drawing a blue marble is $\text{P}\left(\text{B}\right)\text{=}\frac{2}{7}$ .

4.

To determine

To determine the probability of drawing a red or a blue marble.

Answer to Problem 7E

Hence, the probability of drawing a red or a blue marble is $\text{P}\left(\text{A or B}\right)=\frac{1}{2}$ .

Explanation of Solution

Given information:

The given statement is:

“A bag contains $3$ red marbles, $4$ black marbles, $4$ blue marbles and $3$ yellow marbles. You randomly draw a marble from the bag.”

Formula used:

The following formula is used:

  $\text{P}\left(\text{A or B}\right)=\text{P}\left(\text{A}\right)+\text{P}\left(\text{B}\right)$

Calculation:

The probability of drawing a red or a blue marble is:

  $\begin{array}{l}\text{Total number of possible outcomes}=3+4+4+3=14\\ \text{Number of events of drawing a red or a blue marble}=3+4=7\\ \text{Probability of drawing a red or a blue marble P}\left(\text{A or B}\right)=\text{P}\left(\text{A}\right)+\text{P}\left(\text{B}\right)\text{=}\frac{7}{14}=\frac{1}{2}\end{array}$

Hence, the probability of drawing a red or a blue marble is $\text{P}\left(\text{A or B}\right)=\frac{1}{2}$ .