Chapter 13.10, Problem 16PPS

To determine

The probability of each outcome as the card is drawn.

  $P\left(\text{2 or}\text{greater}\text{than}\text{or}\text{equal}\text{to}\text{5}\right)$

Answer to Problem 16PPS

The probability of each outcome as the card is drawn is $P\left(\text{2 or}\text{greater}\text{than}\text{or}\text{equal}\text{to}\text{5}\right)$

  $\frac{5}{7}$

Explanation of Solution

Given:

Digits: $1,2,4,5,7,8,9.$

Concept used:

the objective is to find the probability of every single outcome using this,

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)$

Calculation:

First consider the equation as follows $P\left(\text{2 or}\text{greater}\text{than}\text{or}\text{equal}\text{to}\text{5}\right)$

The given cards are as $1,2,4,5,7,8,9.$ the total of the number of cards is $7$ .

As there are $4$ cards are greater than or equal to $5$ among the $7$ cards.

So, with the help of these the probability as follows:

  $P\left(\text{2 or}\text{greater}\text{than}\text{or}\text{equal}\text{to}\text{5}\right)$ : $P\left(2\right)+P\left(\text{greater}\text{than}\text{or}\text{equal}\text{to}\text{5}\right)$

  $\begin{array}{l}=\frac{1}{7}+\frac{4}{7}\\ =\frac{5}{7}\end{array}$

Conclusion:

Hence, the probability of $2$ or greater than or equal to $5$ is $\frac{5}{7}$ .