- #1

nishantve1

- 76

- 1

## Homework Statement

E1 and E2 are two independent events. The probabilities of an error in judgement by a person regarding E1 and E2 are 0.02 and 0.05 respectively. Find the probability that the person will take the correct decision regarding :

only one event

## Homework Equations

Two events are independent if occurrence of one is not affected by the other and vice versa .

Let,

C1 be the probability the person judging first one right = (1-0.02) = 0.98

C2 be the probability the person judging the second one right = (1-0.05) = 0.95

## The Attempt at a Solution

So if the person judges one event correctly this means the he either judges the first one correctly or the second one correctly

P(only one event) = P(C1 or C2) = P(C1 + C2) =P(C1) + P(C2) - P(C1).P(C2)

=0.999

Which is the wrong anwer . But what's wrong with the logic ?

The hint shows

P(only one event) =

P(E1 is judged correctly and E2 is not judged correctly or E2 is judged correctly and E1 is not judged correctly)

How are these two logics different I mean the first one also finds the probability of one event judgement to be true . Doesn't it ?

Correct answer : 0.068