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 = [tex]2+4+3+1[/tex]
= [tex]10[/tex]
The probability of getting a blue pen is:
[tex]P(\text{Blue})=\dfrac{\text{Number of blue pens}}{\text{Total number of pens}}[/tex]
[tex]P(\text{Blue})=\dfrac{4}{10}[/tex]
[tex]P(\text{Blue})=0.4[/tex]
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.
[tex]P(\text{Blue and Blue})=P(\text{Blue})\times P(\text{Blue})[/tex]
[tex]P(\text{Blue and Blue})=0.4\times 0.4[/tex]
[tex]P(\text{Blue and Blue})=0.16[/tex]
Therefore, the value of [tex]P(\text{Blue and Blue})[/tex] is 0.16.
