Question

Two dice are thrown and it is known that the first die shows a 6. Find the probability that the sum of the numbers showing on two dice is 7.

Answer 1

Consider the given events.
A = First die shows 6
B = The sum of the numbers on two dice is 7.

Clearly,
A= {(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
B = {(2, 5), (5, 2), (4, 3), (3, 4), (1, 6), (6, 1)}

\[\text{ Now } , \]

\[A \cap B = \left\{ \left( 6, 1 \right) \right\}\]

\[ \therefore \text{ Required probability } = P\left( B/A \right) = \frac{n\left( A \cap B \right)}{n\left( A \right)} = \frac{1}{6}\]