Question

Determine if events A and B are mutually exclusive.

P(A) = 1/4 P(B) = 3/5 P(A or B) = 7/10
A) Not mutually exclusive
B) Mutually exclusive

Answer 1

A) Not mutually exclusive

Explanation:

Given

`P(A) = (1)/(4)`

`P(B) = (3)/(5)`

`P(A\ or\ B) = (7)/(10)`

Required

Determine if they are mutually exclusive or not

Mutually exclusive are defined by:

`P(A\ or\ B) = P(A) + P(B)`

So, we have:

`P(A\ or\ B) = (1)/(4) + (3)/(5)`

Take LCM

`P(A\ or\ B) = (5+12)/(20)`

`P(A\ or\ B) = (17)/(20)`

By comparing:

`P(A\ or\ B) = (17)/(20)` ---- Calculated

`P(A\ or\ B) = (7)/(10)` ---- Given

We can conclude that A and B are not mutually exclusive because:

`(17)/(20) \\e (7)/(10)`