Chapter 13.3, Problem 36AYU

For Problems 35 and 36, an urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles.

If one marble is selected, determine the probability that it is black.

To determine

The probability that the selected marble is black.

Answer to Problem 36AYU

$P\left(E\right)=\frac{7}{30}$

Explanation of Solution

Given:

An urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles.

One marble is selected from the urn.

Formula used:

If $S$ is the sample space of this experiment,

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Calculation:

The sample space has 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles $n\left(S\right)=5+10+8+7=30$.

$E=\left\{7Blackmarbles\right\},n\left(E\right)=7$

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

$n\left(E\right)=7,n\left(S\right)=30$

$P\left(E\right) = \frac{7}{30}$