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

Answer:

$P(A \cap B)$

And we can use the following formula:

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

And replacing the info we got:

$P(A \cap B) = \frac{5}{7} \frac{2}{3}= \frac{10}{21}=0.476$

Step-by-step explanation:

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

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

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

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:

$P(A \cap B) = \frac{5}{7} \frac{2}{3}= \frac{10}{21}=0.476$