UPSC NDA Math Model Paper 8

In the given case
Case A: The person is reported 2
Case E1: The number on dice is 2
∴P(E1)=

1

6

Case E2: The number on dice is not2
∴P(E2)=

5

6

Man reported 2 and 2 appears, i.e., man speaking true
⇒P(A|E1)=

3

4

Man reported 2 and 2 do not appears, i.e., man speaking false
⇒P(A|E2)=

1

4

For 2 actually appeared
⇒P(E1|A)=

3 4 × 1 6

3 4 × 1 6 + 1 4 × 5 6

⇒P(E1|A)=

3

8