Question

Two dice are rolled. What is the probability of getting a sum of 3 or 8?

Answer 1

To find the probability of getting a sum of 3 or 8:

It is given that,

Two dice are rolled.

So, the total sample space, n(s)=36.

A be the event of getting a sum of 3.

So, A={(1,2), (2,1)}

n(A)=2

B be the event of getting a sum of 8.

So, B={(2,6), (3,5), (4,4), (5,3), (6,2)}

n(B)=5.

n(AnB)=0.

Using the formula,

$\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ =\frac{n(A)}{n(S)}+\frac{n(A)}{n(S)}-\frac{n(A\cap B)}{n(S)} \\ =\frac{2}{36}+\frac{5}{36}-0 \\ =\frac{7}{36} \end{gathered}$

Hence, the answer is,

$\frac{7}{36}$