Question

two independent, fair 6 sided dice are rolled. the first die face shows a 6. the second die rolls under the table, so you can not see its face. the probability that the dice under the table is 6 given that the first dice is 6 can be written as a fraction a/b, what is such fraction?

Answer 1

The probability that the dice under the table is 6 given that the first dice is 6 can be calculated using Bayes' theorem. Bayes' theorem states that the probability of event B given event A is equal to the probability of event A and event B occurring together divided by the probability of event A.

In this case, the probability of event A is the probability that the first dice shows a 6, which is 1/6. The probability of event B is the probability that the second dice shows a 6, which is also 1/6. The probability of event A and event B occurring together is the probability that both dice show 6, which is (1/6) * (1/6) = 1/36.

Using Bayes' theorem, we can calculate the probability of event B given event A as:

P(B | A) = P(A and B) / P(A) = (1/36) / (1/6) = 1/6

So the probability that the dice under the table is 6 given that the first dice is 6 can be written as a fraction 1/6.