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

Answer:

Probability of exactly 3 red balls = 0.2652

Step-by-step 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 = $^{5} C_3$ = $\frac{5!}{3!*2!}$ = 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 = $^{7} C_2$ = $\frac{7!}{2!*5!}$ = 21

The total number of ways of selecting 5 balls from total of 12 balls in the urn = $^{12} C_5$  = $\frac{12!}{5!*7!}$ = 792

So, probability that your hand has exactly 3 red balls = $\frac{^{5} C_3* ^{7} C_2}{^{12} C_5}$

                                                                                         = $\frac{10*21}{792}$ = 0.2652 .