Consider the following statements related to the nature of Bayes' theorem
1. Bayes' theorem is a formula for computation of a conditional probability.
2. Bayes' theorem modifies an assumed probability of an event in the light of a related event which is observed. Which of the statements given above is/are correct ?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

C

Explanation

Baye's theorem says
if `A_(1), A_(2), .., A_(n)` are (n) mutually exclusive and exhaustive events in sample space S and E is any event is S intersecting events
`A_(i) (iz 1, 2, .., n)` such that `P(E) ne 0` then
`P(A_(i) //E) = (P(E//A_(i)))/(P(E))`
`= (P(A_(i))P(E//A_(i)))/(overset(n)underset(|2|)sum P(A_(i))P(E//A_(i)))`