Chapter 13.10, Problem 32STP

To determine

The probability of the P (red, white).

Answer to Problem 32STP

The probability of the $P\left(\text{red,white}\right)\text{=0}\text{.083}$ .

Explanation of Solution

Given:

Blue: $5$

Red: $4$

White: $3$

Total marbles: $5+4+3=12$

Calculation:

The objective is to get the probability of the red and white marbles as follows:

Red and white are two independent events.

There are $4$ red and $3$ white marbles.

  $\begin{array}{l}P\left(\text{red,white}\right)\text{=}P\left(\text{red}\right)\times P\left(\text{white}\right)\\ P\left(\text{red,white}\right)\text{=}\frac{\text{4}}{\text{12}}\text{×}\frac{\text{3}}{\text{12}}\\ P\left(\text{red,white}\right)\text{=}\frac{\text{12}}{\text{144}}\\ P\left(\text{red,white}\right)\text{=0}\text{.083}\end{array}$

Therefore the $P\left(\text{red,white}\right)\text{=0}\text{.083}$

Conclusion:

Hence, $P\left(\text{red,white}\right)\text{=0}\text{.083}$ .