Question

A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

(a) 1/4
(b) 1/3
(c) 1/2
(d) 2/3

Answer 1

The probability that it is actually a six is 1/2. (c) 1/2 is the correct answer.

Step-by-step explanation:

To find the probability that the man's report of a six is actually a six, we need to consider both the probability of him speaking the truth and the probability of rolling a six on a fair six-sided die.

The man is known to speak the truth 3 out of 4 times, so the probability of him speaking the truth is 3/4. The probability of rolling a six on a fair six-sided die is 1/6.

Now, let's use Bayes' theorem to find the probability that it is actually a six. Bayes' theorem is given by:

P(A|B) = (P(B|A) * P(A)) / P(B)

In this case, A represents the event that the man speaks the truth (reporting a six) and B represents the event of actually rolling a six. Plugging in the values, we have:

P(A|B) = (3/4 * 1/6) / (1/4)

This simplifies to:

P(A|B) = 1/2

Therefore, the probability that it is actually a six is 1/2.