Chapter 12.8, Problem 1P

(a)

To determine

To find: The probability $P\left(\text{even}\text{or}\text{less}\text{than}\text{4}\right)$

Answer to Problem 1P

The probability $P\left(\text{even}\text{or}\text{less}\text{than}\text{4}\right)$ is $\frac{5}{6}$

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 $P\left(\text{even}\text{or}\text{less}\text{than}\text{4}\right)$ is calculated as,

  $\begin{array}{c}P\left(\text{even}\text{or}\text{less}\text{than}\text{4}\right)=P\left(\text{even}\right)+P\left(\text{less}\text{than}\text{4}\right)\\ =\frac{3}{6}+\frac{2}{6}\\ =\frac{5}{6}\end{array}$

Therefore, the probability of $P\left(\text{even}\text{or}\text{less}\text{than}\text{4}\right)$ is $\frac{5}{6}$ .

(b)

To determine

To find: The probability $P\left(\text{2}\text{or}\text{odd}\text{number}\right)$

Answer to Problem 1P

The probability $P\left(\text{2}\text{or}\text{odd}\text{number}\right)$ is $\frac{2}{3}$

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 $P\left(\text{2}\text{or}\text{odd}\text{number}\right)$ is calculated as,

  $\begin{array}{c}P\left(\text{2}\text{or}\text{odd}\text{number}\right)=P\left(\text{2}\right)+P\left(\text{odd}\text{number}\right)\\ =\frac{1}{6}+\frac{3}{6}\\ =\frac{4}{6}\\ =\frac{2}{3}\end{array}$

Therefore, the probability of $P\left(\text{2}\text{or}\text{odd}\text{number}\right)$ is $\frac{2}{3}$ .