Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls. Find the probability that (a) 3 red, 2 blue, and 2 green balls are withdrawn; (b) at least 2 red balls are withdrawn; (c) all withdrawn balls are the same color; (d) either exactly 3 red balls or exactly 3 blue balls are withdrawn.

a) P=0.226

b) P=0.6

c) P=0.0008

d) P=0.74

Step-by-step explanation:

We know that the seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls. Therefore, we have 46 balls.

a) We calculate the probability that are 3 red, 2 blue, and 2 green balls.

We calculate the number of possible combinations:

We calculate the number of favorable combinations:

Therefore, the probability is

b) We calculate the probability that are at least 2 red balls.

We calculate the probability  withdrawn of 1 or none of the red balls.

We calculate the number of possible combinations:

We calculate the number of favorable combinations: for 1 red balls

Therefore, the probability is

We calculate the number of favorable combinations: for none red balls

Therefore, the probability is

Therefore, the  the probability that are at least 2 red balls is

c) We calculate the probability that are all withdrawn balls are the same color.

We calculate the number of possible combinations:

We calculate the number of favorable combinations:

Therefore, the probability is

d) We calculate the probability that are either exactly 3 red balls or exactly 3 blue balls are withdrawn.

Let X, event that exactly 3 red balls selected.

Let Y, event that exactly 3 blue balls selected.

We have

Therefore, we get