Question

If two fair dice are rolled find the probabilities of the following
1. sum greater than or equal to 9 given that the roll was a double
2. a double given that the sum was strictly greater than 9

Answer 1

1. If 2 fair dice are rolled hence total of 36 sample outcome will appear

if we look at sum is 9 or grater than the no of outcomes are as10

sample space can be computed as

hence P(Sum=9 or more than 9)=10/36

Roll is double D1D2(Pair)= 6 times hence

P(Pair)=6/36=1/6

The intersection : sum= {55,66} hence P=2/36=1/18

hence according to question

P(sum|roll is double)=

=1/3=0.333

2).P(Double given that strictly greater than 9)

P(Double )=1/6 as calculated above.

P(Sum>9)= 6/36=1/6 as sample of Sum>9 is 6

again intersection =1/18

Now according to question

P(double | Sum>9) =

=0.333