Chapter 8.6, Problem 16E

To determine

To find the probability of getting a black card.

Answer to Problem 16E

The probability of getting a black card is $\frac{1}{2}$ .

Explanation of Solution

Given:

A card is drawn at random from a standard deck of 52 playing cards.

Calculation:

Number of outcomes in the sample space is 52.

  $\therefore n\left(S\right)=52$

Let B be the event of getting a black card.

Since there are 26black cards.

  $\therefore n\left(B\right)=26$

Hence the probability of getting a black card is,

  $\begin{array}{l}P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}\\ \Rightarrow P\left(B\right)=\frac{26}{52}\\ \Rightarrow P\left(B\right)=\frac{1}{2}\end{array}$