Chapter 13, Problem 21SGR

To determine

Find the probability of drawing 2 black marbles and 1 white marble in a row without repetition if the box contains a total of 3 white marbles and 4 black marbles.

Answer to Problem 21SGR

The probability of drawing two black marbles and 1 white marble without repetition is $\frac{6}{35}$ .

Explanation of Solution

Given information: It is given that the box contains 3 white marbles and 4 black marbles.

Calculation: Since the box contains 3 white and 4 black marbles. Therefore the probability of drawing 2 black marbles and 1 white marble without repetition is evaluated as,

  $\begin{array}{c}P\left(2B\text{ and }1W\right)=\left(\frac{4}{7}\right)\left(\frac{3}{6}\right)\left(\frac{3}{5}\right)\\ =\frac{36}{210}\\ =\frac{6}{35}\end{array}$

Hence the probability of drawing two black marbles and 1 white marble without repetition is $\frac{6}{35}$ .