Question

The probability of rolling a sum of 7 when rolling two dice simultaneously is 0.167. You decide to test that probability by rolling the dice 12 times. What is the probability that exactly 2 of the rolls is a sum of 7?

Answer 1

The probability that exactly 2 of the rolls is a sum of 7 will is 0.296

Explanation:

The probability of rolling a sum of 7 when rolling two dice simultaneously is 0.167.

Let us assume that, A be the event that the sum is 7. So,

`P(A)=0.167`

Binomial probability represents the probability that a binomial experiment results (i.e either success or failure or only two results) in exactly x successes.

`b(x;\ n, p) =\ ^nC_x \cdot p^x \cdot (1-p)^(n - x)`

So the probability that exactly 2 of the rolls is a sum of 7 will be,

`P(2) =\ ^(12)C_2 \cdot (0.167)^2 \cdot (1-0.167)^(12 - 2)`

`=\ ^(12)C_2 \cdot (0.167)^2 \cdot (0.833)^(10)`

`=66 \cdot (0.167)^2 \cdot (0.833)^(10)`

`=0.296`