Question

if A and B are independent events where P(A) = 0.7 and P(B)= .8:

1. P(A ^ B) =

2. P(~A^~B) =

3.P(A U B) =

4. Does your anwser change if they were dependent?

Answer 1

In this case we have given A and B is independent with P(A)=0.7, P(B)=0.8.

1. For independent event we know that

2. The probability P(~A^~B) indicates the probability of complement of A and complement of B given by

Therefore for obtaining the probability of , we first obtain the value of .

Therefore, the probability of event

3) For obtaining this probability we make use of addition theorem of probability and hence the probability is given by

Therefore the value for is 0.94.

4.We can see from the above that each probability depends on the intersection of the value and hence it's value changes in case of dependent of the event.

So, all values changes.