Respuesta :
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:
[tex]P(D\cup S8)=P(D)+P(S8)-P(D\cap S8)[/tex]
[tex]=\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[/tex]
Thus, the probability of rolling a doubles or getting two numbers whose sum is equal to 8 is 0.278.
