Question

A fair coin is tossed .if the coin is tails one die is rolled and the number on the die is recorded if the coin toss is heads two die are rolled and the sum of the numbers on two independent fair dice is recorded
Whaat is the probability the result is 9?

Answer 1

So for the dice to be 9 two die must be rolled. So we start with a 1/2 chance.

Then there are 36 possibilities to be rolled on a die (6*6) and there are 4/36 possibilities for the dice to roll a 9 (4+5, 5+4, 3+6, 6+3).

So we multiply 1/2 by 1/9 (4/36)- which equals 1/18.

So there is a 1/18 chance for the result of the dice rolled to be a 9.

I hope this helps!