Question

A bag contains 7 blue, 3 green, and 3 red marbles. If Agnes randomly draws two marbles from the bag, replacing the first before drawing the second, what is the probability of drawing a green and then a blue marble?

Answer 1

`(21)/(169)`

Explanation:

Given:

Number of blue marbles in a bag = 7

Number of green marbles in a bag = 3

Number of red marbles in a bag = 3

Agnes randomly draws two marbles from the bag, replacing the first before drawing the second.

To find:

the probability of drawing a green and then a blue marble

Solution:

Let A denotes the event of drawing a green marble and B denotes the event of drawing a blue marble

`P(A)=(3)/(13)\\ P(B)=(7)/(13)`

As Agnes randomly draws two marbles from the bag, replacing the first before drawing the second, so A and B are independent events.

So, the probability of drawing a green and then a blue marble

`=P(A)P(B)\\=((3)/(13) )((7)/(13) )=(21)/(169)`