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
Answer:
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
