Chapter 10.4, Problem 11E

To determine

Tocalculate:

The probability of randomly drawing a card from the $52$ playing cards.

Answer to Problem 11E

The probability of randomly drawing a card from the $52$ playing cards is $0.42$ .

Explanation of Solution

Given information:

  $\begin{array}{l}P\left(heartorfacecard\right)\\ =P\left(heart\right)+P\left(facecard\right)\\ =\frac{13}{52}+\frac{12}{52}=\frac{25}{52}\end{array}$

Formula used:

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

Calculation:

There are $52$ cards. Assume that event $A$ denote heart card and event $B$ denote face card. With the help of given information $3$ cards are common to both $A$ and $B$ . Then probability of $A$ or $B$ is given as follows:

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

The given solution does not take into account the probability of the common events. Therefore, the required probability is as follows:

  $\begin{array}{l}P\left(AorB\right)=\frac{13}{52}+\frac{12}{52}-\frac{2}{52}\\ =\frac{22}{52}\\ =0.42\end{array}$

Hence, the answer is $0.42$ .

So, the probability of randomly drawing a card from the $52$ playing cards is $0.42$ .