Question

Conditional Probability - A Die and a Coin (Part b)

b) A die and a coin. Bob rolls a single six-sided die and then flips a coin a number of times equal to the number showing on the die. The coin comes up heads every time. What is the probability that the die showed 1?

Answer 1

The probability that the die showed 1 given that the coin came up heads every time is 1/12.

Step-by-step explanation:

To find the probability that the die showed 1 given that the coin came up heads every time, we can use conditional probability. Let's denote the event that the die showed 1 as A and the event that the coin came up heads every time as B. The probability of event A given event B is equal to the probability of A and B occurring divided by the probability of event B.

Since the coin came up heads every time, event B has a probability of 1. As for event A, there is only one outcome out of the possible 12 outcomes where the die shows 1 and the coin comes up heads every time. Therefore, the probability of event A and B occurring is 1/12. Therefore, the probability that the die showed 1 given that the coin came up heads every time is 1/12.