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

Answer:

The probability that A and B both occur events

$P(An B) = \frac{10}{21}=0.4761$

Step-by-step explanation:

Explanation:-

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

$P(A) = \frac{5}{7}$

The probability that even B occurs is 2/3

$P(B) = \frac{2}{3}$

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)

                                             $P(A nB) = \frac{5}{7} X \frac{2}{3}$

                                             $P(An B) = \frac{10}{21}$

                                         $P(An B) = \frac{10}{21}=0.4761$

                                             

Conclusion:-

The probability that A and B both occur events

$P(An B) = \frac{10}{21}=0.4761$