Question

Warren has a container which holds 22 books of the same shape and size. The exact breakdown of his books is shown below:

6 white books
9 purple books
7 green books
Each time, Warren takes out a book at random. He will replace the book and take out another book from the container. What is the probability that Warren takes out a green book in both draws? (3 points)

a
7 over 22 multiplied by 7 over 22 equal 49 over 484

b
7 over 22 multiplied by 6 over 21 equal 42 over 462

c
7 over 22 plus 6 over 21 equal 279 over 462

d
7 over 22 plus 7 over 22 equal 308 over 484

Answer 1

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,

`\text{Probability}=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}`

`P(\text{White})=(6)/(22)`

`P(\text{Purple})=(9)/(22)`

`P(\text{green})=(7)/(22)`

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:

`P=P(\text{green})* P(\text{green})`

`P=(7)/(22)* (7)/(22)`

`P=(49)/(484)`

Therefore, the correct option is (a).