Question

A bag contains 5 red marbles and 4 green marbles.

What is the probability of choosing a red marble then a green marble, without replacement?

Answer 1

Answer: The required probability is
`(5)/(18).`

Step-by-step explanation: Given that a bag contains 5 red marbles and 4 green marbles.

We are to find the probability of choosing a red marble then a green marble, without replacement.

Total number of balls in the bag = 5 + 4 = 9.

The probability of choosing a red marble is given by

`P_r=\frac{\textup{number of red balls}}{\textup{total number of balls}}=(5)/(9).`

Since the second balls is chosen without replacing the first ball, so

the total number of balls remained in the bag = 4 + 4 = 8.

And the probability of choosing a green ball without replacement is

`P_g=\frac{\textup{number of green balls}}{\textup{total number of balls remained in the bag}}=(4)/(8)=(1)/(2).`

Therefore, the probability of choosing a red marble then a green marble, without replacement is given by

`P=P_r* P_g=(5)/(9)* (1)/(2)=(5)/(18).`

Thus, the required probability is
`(5)/(18).`