Question

A drawer contains 6 pink gloves and 5 yellow gloves. What is the probability that you select two pink gloves if you reach in the drawer and randomly grab two gloves without replacement?

1/11

1/30

2/11

3/11

1/15

Answer 1

`(3)/(11)`

Explanation:

Given that:

A drawer contains 6 pink and 5 yellow gloves.

Two gloves are randomly drawn without replacement.

To find:

The probability that the two gloves drawn are both pink.

Solution:

First of all, let us have a look at the formula for Probability of an event E:

Formula for probability of an event E can be observed as:

`P(E) = \frac{\text{Number of favorable cases}}{\text {Total number of cases}}`

Here, number of favorable cases are to draw 2 pink gloves out of 6, which is equal to:

`_6C_2 = (6* 5)/(2) = 15`

Here, Total number of cases are to draw 2 gloves out of 11, which is equal to:

`_(11)C_2 = (11* 10)/(2) = 55`

Now, the required probability is:

`P(2\ pink\ gloves) = (15)/(55)\\\Rightarrow P(2\ pink\ gloves) = (3)/(11)`

Therefore, the answer is:

`(3)/(11)`