Given:
Total number of book = 22
Number of white books = 6
Number of Purple books = 9
Number of green books = 7
To find:
The probability that Warren takes out a green book in both draws (with replacement).
Solution:
We know that,
[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]P(\text{White})=\dfrac{6}{22}[/tex]
[tex]P(\text{Purple})=\dfrac{9}{22}[/tex]
[tex]P(\text{green})=\dfrac{7}{22}[/tex]
After replacement, the probability of event remains the same and the independent.
The probability that Warren takes out a green book in both draws is:
[tex]P=P(\text{green})\times P(\text{green})[/tex]
[tex]P=\dfrac{7}{22}\times \dfrac{7}{22}[/tex]
[tex]P=\dfrac{49}{484}[/tex]
Therefore, the correct option is (a).
