Question

Q5: The probability that event A occurs is 5/7 and the probability that event B occurs is 2/3 . If A and B are independent events, what is the probability that A and B both occur?

Answer 1

`P(A \cap B)`

And we can use the following formula:

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

And replacing the info we got:

`P(A \cap B) = (5)/(7) (2)/(3)= (10)/(21)=0.476`

Explanation:

We define two events for this case A and B. And we know the probability for each individual event given by the problem:

`p(A) = (5)/(7)`

`p(B) = (2)/(3)`

And we want to find the probability that A and B both occurs if A and B are independent events, who menas the following conditions:

`P(A|B) = P(A)`

`P(B|A) = P(B)`

And for this special case we want to find this probability:

`P(A \cap B)`

And we can use the following formula:

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

And replacing the info we got:

`P(A \cap B) = (5)/(7) (2)/(3)= (10)/(21)=0.476`