Question

Suppose A and B are independent events. If P(A) = 0.3 and P(B) = 0.9, what is P(AuB)?

Answer 1

`P(A\cup B)=0.93`

Explanation:

We have been given that A and B are independent events. We are asked to find
`P(A\cup B)`.

We know that if two events are independent, then
`P(A\cup B)=P(A)+P(B)-P(A\cap B)`.

`P(A\cap B)=P(A)*P(B)`

Substituting our given values in above formula we will get,

`P(A\cup B)=0.3+0.9-(0.3*0.9)`

`P(A\cup B)=1.2-0.27`

`P(A\cup B)=0.93`

Therefore, the probability of
`P(A\cup B)` is 0.93.

Answer 2

When the events are independent
P(A∪B) = P(A) + P(B) - P(A∩B) . . . . where P(A∩B) = P(A)·P(B)

Substituting the given numbers, you have
P(A∪B) = 0.3 + 0.9 - 0.3·0.9
P(A∪B) = 0.93