Probability:

Question

involving the sum of the numbers showing on two fair dice.
(1) What is the probability that exactly one die shows a 2 given that the sum of the numbers is 8?


(2) What is the probability that the sum of the numbers is 8 given that exactly one die shows a 2?


(3) What is the probability that the sum of the numbers is 8 given that at least one die shows a 2?

Answer 1

 1) if the sum is 8 ,it means these are the possibilities..

 

2,6

3.5

4,4

5,3

6,2

 

out of these 5 possibilities  2 are favouring your condition

so ans is 2/5

 

 

2) if exactly one dice shows 2 it means

2,1

2,3

2,4

2,5

2,6

1,2

3,2

4,2

5,2

6,2

ie 10 possibilities

 

out of them  2 are such that sum is 8 

so ans is 

2/10

ie 1/5

 

3)if atleast one dice shows 2 ,then along with the 10 written for part 2 ,we can have 

2,2 also

 

so 11 possibilities

out of them 2 favour 

 

so ans is 2/11