# Max has 4 blue shirts, 3 red shirts, and 5 striped shirts. What is the probability that he will select a red shirt and then a striped shirt without replacement?

Apr 19, 2018

$\frac{5}{44}$

#### Explanation:

For probability questions, you first need to add up all the possible outcomes. In this case, the total number of shirts that Max can pick from.

$4 + 3 + 5 = 12$

Now, find the probability of Max choosing a red shirt from the 12 total shirts.

Red: $\frac{3}{12} = \frac{1}{4}$

Since the problem states that there is no replacement, you must recalculate the total number of shirts.

$12 - 1 = 11$

Now, find the probability of Max choosing a striped shirt from the 11 remaining shirts.

Striped: $\frac{5}{11}$

To find the probability of both events happening, multiply the two probabilities.

1/4*5/11=5/(4*11)=5/44 approx 11%

This is the probability that Max will pick a red shirt then a striped shirt without replacing anything.

Apr 19, 2018

$\frac{5}{44}$

#### Explanation:

We need to find the probability of choosing a red shirt, and the probability of choosing striped shirt. Then we will multiply them together.

The chance that he will pick a red shirt would be:

$\text{number of red shirts"/"total number of shirts} \rightarrow \frac{3}{4 + 3 + 5} \rightarrow \frac{3}{12} \rightarrow \frac{1}{4}$

The chance he will pick a striped shirt without replacement would be:

$\text{number of striped shirts"/"new total number of shirts}$

Since he already took a shirt away, the total number of shirts would now be $11$ instead of $12$, so the ratio would be:

$\frac{5}{11}$

Now multiply the two probabilities together:

$\frac{1}{4} \cdot \frac{5}{11} = \frac{5}{44}$

The probability is $\frac{5}{44}$