Question

A bag contains 2 red pens, 4 blue pens, 3 black pens, and 1 green pen. Once a pen is selected, it is replaced, and then another pen is selected. Determine P(blue and blue)

Answer 1

Given:

A bag contains 2 red pens, 4 blue pens, 3 black pens, and 1 green pen.

Once a pen is selected, it is replaced, and then another pen is selected.

To find:

The probability of getting blue pens in both draws, i.e., P(blue and blue).

Solution:

We have,

Number of red pens = 2

Number of blue pens = 4

Number of black pens = 3

Number of green pen = 1

Total number of pens =
`2+4+3+1`

=
`10`

The probability of getting a blue pen is:

`P(\text{Blue})=\frac{\text{Number of blue pens}}{\text{Total number of pens}}`

`P(\text{Blue})=(4)/(10)`

`P(\text{Blue})=0.4`

Once a pen is selected, it is replaced, and then another pen is selected. So, after replacement the probability of getting a blue is remains the same.

`P(\text{Blue and Blue})=P(\text{Blue})* P(\text{Blue})`

`P(\text{Blue and Blue})=0.4* 0.4`

`P(\text{Blue and Blue})=0.16`

Therefore, the value of
`P(\text{Blue and Blue})` is 0.16.