If P (A) = 0.5, P (A∪B) = 0.8 and P (A∩B) = 0.4 then find P (B).

P (B) =

First of all, this is a probability question, so you must memorize the rules.

P (B) = P (AUB) + P (A int. B) - P (A)

=0.8+0.4-0.5

P (B) = 0.7

Therefore, P (B). P (B) = 0.7*0.7=0.49

P (B) = 0.7

Step-by-step explanation:

for events that are NOT mutually exclusive, the following applies:

P (A∪B) = P (A) + P (B) - P (A∩B)

in our case we can see that P (A∩B) is given as non-zero, hence the events are not mutually exclusive and the above formula can be used.

Given:

P (A) = 0.5

P (A∪B) = 0.8

P (A∩B) = 0.4

Substituting these into the above equation

P (A∪B) = P (A) + P (B) - P (A∩B)

0.8 = 0.5 + P (B) - 0.4

0.8 = 0.1 + P (B) (subtract 0.1 from both sides)

P (B) = 0.8 - 0.1 = 0.7