Question

An urn has 5 red balls and 7 blue balls. Suppose you randomly select 5 balls from the urn. What is the probability that your hand has exactly 3 red balls

Answer 1

Probability of exactly 3 red balls = 0.2652

Explanation:

We are given that an urn has 5 red balls and 7 blue balls.

And we randomly select 5 balls from the urn and have to find the probability that your hand has exactly 3 red balls.

Firstly, number of ways of selecting 3 red balls from total of 5 red balls in the urn =
`^(5) C_3` =
`(5!)/(3!*2!)` = 10

Now since 5 balls have to be selected so remaining 2 balls will be blue only, so number of ways of selecting 2 blue balls from total of 7 blue balls in the urn =
`^(7) C_2` =
`(7!)/(2!*5!)` = 21

The total number of ways of selecting 5 balls from total of 12 balls in the urn =
`^(12) C_5` =
`(12!)/(5!*7!)` = 792

So, probability that your hand has exactly 3 red balls =
`(^(5) C_3* ^(7) C_2)/(^(12) C_5)`

=
`(10*21)/(792)` = 0.2652 .