Question

Event A has a 0.3 probability of occuring and event B has a 0.4 probability of occuring. A and B are independent events. What is the probability that either A or B occurs?

0.42

0.54

0.70

0.12

Answer 1

When you say either, you add both A and B
0.3+0.4=0.7
Your answer is 0.70 which means 70%

Answer 2

The probability that either A or B occurs is 0.58

Explanation:

P(A) = 0.3

P(B) =0.4

Since we are given that A and B are independent events

So, P(A∩B)=P(A)*P(B)

P(A∩B)=0.3*0.4=0.12

So, P(A∪B)= P(A)+P(B)-P(A∩B)

P(A∪B)= 0.3+0.4-0.12

P(A∪B)=0.7-0.12

P(A∪B)=0.58

Now, the probability that either A or B occurs (or both occurs) = P(A∪B)+P(A∩B)

= 0.58

Thus,the probability that either A or B occurs is 0.58