Question

Two dice are rolled; find the probability of rolling a doubles (2 of a kind) or getting two numbers whose sum is equal to 8.

Answer 1

Answer:

The probability of rolling a doubles or getting two numbers whose sum is equal to 8 is 0.278.

Step-by-step explanation:

There are a total of N = 36 outcomes when rolling two fair dice.

The outcomes for rolling doubles are: {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}.

So, n (Doubles) = n (D) = 6

The outcomes for rolling a sum of 8 are: {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}

So, n (Sum 8) = n (S8) = 5

Considering the outcomes of the above two events, it can be seen that there is a common outcome, i.e. (4, 4).

So, n (D ∩ S8) = 1

Compute the probability of rolling a doubles or getting two numbers whose sum is equal to 8 as follows:

$P(D\cup S8)=P(D)+P(S8)-P(D\cap S8)$

                 $=\frac{n(D)}{N}+\frac{n(S8)}{N}-\frac{n(D\cap S8)}{N}\\\\=\frac{6}{36}+\frac{5}{36}-\frac{1}{36}\\\\=\frac{6+5-1}{36}\\\\=\frac{10}{36}\\\\=0.278$

Thus, the probability of rolling a doubles or getting two numbers whose sum is equal to 8 is 0.278.