Chapter 12.8, Problem 1LC

(a)

To determine

To find: The probability of B or number.

Answer to Problem 1LC

The probability of B or number is $\frac{4}{5}$ .

Explanation of Solution

The expression for probability of an event is given by,

  $P\left(E\right)=\frac{\text{Favorable}\text{Outcomes}}{\text{Possible}\text{outcomes}}$

The probability of $P\left(\text{B}\text{or}\text{number}\right)$ is calculated as,

  $\begin{array}{c}P\left(\text{B}\text{or}\text{number}\right)=P\left(B\right)+P\left(\text{Number}\right)\\ =\frac{1}{5}+\frac{3}{5}\\ =\frac{4}{5}\end{array}$

Therefore, the probability of B or number is $\frac{4}{5}$ .

(b)

To determine

To find: The probability of red or 5.

Answer to Problem 1LC

The probability of red or 5 is $\frac{3}{5}$ .

Explanation of Solution

The expression for probability of an event is given by,

  $P\left(E\right)=\frac{\text{Favorable}\text{Outcomes}}{\text{Possible}\text{outcomes}}$

The probability of $P\left(\text{red}\text{or}\text{5}\right)$ is calculated as,

  $\begin{array}{c}P\left(\text{red}\text{or}\text{5}\right)=P\left(\text{red}\right)+P\left(5\right)\\ =\frac{2}{5}+\frac{1}{5}\\ =\frac{3}{5}\end{array}$

Therefore, the probability of red or 5 is $\frac{3}{5}$ .

(c)

To determine

To find: The probability of red or yellow.

Answer to Problem 1LC

The probability of red or yellow is $\frac{3}{5}$ .

Explanation of Solution

The expression for probability of an event is given by,

  $P\left(E\right)=\frac{\text{Favorable}\text{Outcomes}}{\text{Possible}\text{outcomes}}$

The probability of $P\left(\text{red}\text{or}\text{yellow}\right)$ is calculated as,

  $\begin{array}{c}P\left(\text{red}\text{or}\text{yellow}\right)=P\left(\text{red}\right)+P\left(\text{yellow}\right)\\ =\frac{2}{5}+\frac{3}{5}\\ =\frac{5}{5}\\ =1\end{array}$

Therefore, the probability of red or yellow is $1$ .

(d)

To determine

To find: The probability of yellow or letter.

Answer to Problem 1LC

The probability of yellow or letter is $\frac{4}{5}$ .

Explanation of Solution

The expression for probability of an event is given by,

  $P\left(E\right)=\frac{\text{Favorable}\text{Outcomes}}{\text{Possible}\text{outcomes}}$

The probability of $P\left(\text{yellow}\text{or}\text{letter}\right)$ is calculated as,

  $\begin{array}{c}P\left(\text{yellow}\text{or}\text{letter}\right)=P\left(\text{letter}\right)+P\left(\text{yellow}\right)-P\left(\text{yellow}\text{and}\text{letter}\right)\\ =\frac{3}{5}+\frac{2}{5}-\frac{1}{5}\\ =1-\frac{1}{5}\\ =\frac{4}{5}\end{array}$

Therefore, the probability of yellow or letter is $\frac{4}{5}$