Question

A die is thrown three times. Events A and B are defined as below:
A: 6 on the third throw
B: 4 on the first and 5 on the second throw
The probability of A given that B has already occurred, is:

• A. $\frac{1}{6}$
• B. $\frac{2}{3}$
• C. $\frac{3}{4}$
• D. $\frac{1}{2}$

Answer 1

The Correct Option is A

Event \(B\) indicates that the first throw is a 4 and the second throw is a 5. The probability of event \(B\) occurring is independent of event \(A\). Since the die is fair, the probability of rolling a 6 on any throw is \(\frac{1}{6}\).

Therefore, the probability of \(A\) given that \(B\) has already occurred is:

\[ P(A|B) = P(A) = \frac{1}{6}. \]