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

Question

asked Nov 28, 2022 223k views

1 Answer

Bizna · Answer 1 · 2022-12-04T02:22:45+0000

Answer:

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:

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