A die is tossed until the sum of the rolls is 15 or greater.

What is the most likely total? What is the the least likely total which can occur?

The least likely total is 90.

How I arrived at that:
The minimum no of times the die has to be rolled to get a sum >=15 is 3.
The maximum no of times is 15 assuming you get 1 on each throw.

In 3 throws the minimum total is 3, 1 being the number rolled each throw. Probability of this happening is 1/6 * 1/6 * 1/6 = 1/216

In 15 throws the maximum total is 15*6 = 90, the probability of this happening is 1/6 * 1/6 *....(15 times) = (1/6)^15 which is the minimum probability for 15 throws.

Posted by Sohini on 2003-07-26 07:54:26