Question

Jim rolled a fair die five times and obtained a 3 every time. He concluded that on the next roll a 3 is more likely to occur than any other number. Explain whether this is true

Answer 1

Deejilani, this is the solution:

Jim conclusion that on the next roll a 3 is more likely to occur is not true.

Actually, a 3 has the same probability to occur that the other five numbers:

The probabilities are:

P(1) = 1/6

P(2) = 1/6

P(3) = 1/6

P(4) = 1/6

P(5) = 1/6

P(6) = 1/6

As you can see, the probabilities are exactly the same because the die is fair.