Question

There are 10 balls in a bag, 4 red balls and 6 black balls. If you pick one red ball, you will take it without replacement. If you pick one black ball, you will return it into the bag. Now you pick two times and each time you can only take one ball. What is the probability that you will pick two red balls

Answer 1

The probability of selecting two red balls is 0.132.

Explanation:

In a bag there are 10 balls in a bag, 4 red balls and 6 black balls.

The conditions of selecting a ball are:

• If you pick one red ball, you will take it without replacement.
• If you pick one black ball, you will return it into the bag.

It is also provided that only one ball can be picked at a time.

Now, it is given that two balls are picked.

The number of ways to select a red ball in the first draw is:
`{4\choose 1}=4\ \text{ways}`

Compute the probability of selecting a red ball in the first draw as follows:

`P(\text{First ball is Red})=\frac{{4\choose 1}}{{10\choose 1}}=(4)/(10)=0.40`

Now as a red ball is selected it will not be replaced.

So, there are 9 balls in the bag now.

The number of ways to select a red ball in the second draw is:
`{3\choose 1}=3\ \text{ways}`

Compute the probability of selecting a red ball in the second draw as follows:

`P(\text{Second ball is Red})=\frac{{3\choose 1}}{{9\choose 1}}=(3)/(9)=0.33`

Compute the probability of selecting two red balls as follows:

`P(\text{Two Red balls})=P(\text{First ball is Red})* P(\text{Second ball is Red})`

`=0.40* 0.33\\\\=0.132`

Thus, the probability of selecting two red balls is 0.132.