What is the probability that green is rolled exactly 7 times?

Question

On a dice, one side is red, three sides are green and two sides are blue. The dice is also rolled 20 times.

Answer 1

The probability is the ratio between the number of ways of getting a desired outcome

divided by the number of ways to get any outcome.

This is how you calculate the number of ways to get any outcome.

On each throw there are 6 possible outcomes.

For each of the 6 outcomes of the first throw there are 6 possible outcomes

of the second outcome. And so on.

Therefore the number of outcomes get multiplied.

Hence 20 throws have 6²⁰ possible outcomes.

This is how you calculate the number of ways of getting a desired outcome.

First of all, there are "20 chose 7" (= 77520) ways of choosing which of the 20 throws

should yield green.

For a each of the 7 throws chosen there are 3 ways of getting green.

For each of the 13 throws that are to yield something not green,

there are also 3 ways of accomplishing that.

Therefore the number of ways of getting a desired result is

77520×3²⁰

Thus the probability is

77520×3²⁰/6²⁰ = 77520/2²⁰ = 0.074