Question

6. A pair of 10-sided, numbered 1 through 10, dice are rolled. What is the probability that the sum of the two dice is:

a) 18

b) 19, given that a sum of 18 or more was rolled.

Answer 1

Solution:

If we roll pair of 10 sided dice then this event will have 100 outcomes like {(1,1), (1,2) ... (10,9), (10,10)}

a) so now if we want to collect outcomes which are having sum of 18 then total 3 possible outcomes would be {(8,10), (9,9), (10,8)}

So probability P(sum of 18 ) = 3/100 = 0.03

b) let's find out if sum is greater than or equal to 18.

So total 6 events are {(8,10), (9,9), (9,10), (10,8), (10,9), (10,10)}

Now getting probability of sum of 19 would be by considering above as total outcomes, Of which (9,10) and (10,9) is having sum equal to 19.

So P( sum equals to 19) = 2/6 = 0.3333