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

Answer:

$\dfrac{3}{11}$

Step-by-step 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:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

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

$_6C_2 = \dfrac{6\times 5}{2} = 15$

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

$_{11}C_2 = \dfrac{11\times 10}{2} = 55$

Now, the required probability is:

$P(2\ pink\ gloves) = \dfrac{15}{55}\\\Rightarrow P(2\ pink\ gloves) = \dfrac{3}{11}$

Therefore, the answer is:

$\dfrac{3}{11}$