Question

The probability that even A occurs is 5/7 and the probability that even B occurs is 2/3 are independent event's what is the probability that A and B both occur

Answer 1

The probability that A and B both occur events

`P(An B) = (10)/(21)=0.4761`

Explanation:

Explanation:-

Given data the probability that event A occurs is 5/7

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

The probability that even B occurs is 2/3

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

Independent events:-

If the occurrence of the event 'B' is not effected by the occurrence or non-occurrence of the event 'A' , then the event 'B' is said to be independent of A.

A and B are independents events P(A∩B) = P(A) P(B)

The probability that A and B both occur events

P(A∩B) = P(A) P(B)

`P(A nB) = (5)/(7) X (2)/(3)`

`P(An B) = (10)/(21)`

`P(An B) = (10)/(21)=0.4761`

Conclusion:-

The probability that A and B both occur events

`P(An B) = (10)/(21)=0.4761`