Question

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?

Answer 1

`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: `3/12=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: `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.

Answer 2

`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:

`"number of red shirts"/"total number of shirts" rarr 3/(4 + 3 + 5) rarr 3/12 rarr 1/4`

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

`"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:

`5/11`

Now multiply the two probabilities together:

`1/4 * 5/11 = 5/44`

The probability is `5/44`