Answer:
[tex] P(A \cap B)[/tex]
And we can use the following formula:
[tex] P(A \cap B)= P(A)* P(B)[/tex]
And replacing the info we got:
[tex] P(A \cap B) = \frac{5}{7} \frac{2}{3}= \frac{10}{21}=0.476[/tex]
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:
[tex] p(A) = \frac{5}{7}[/tex]
[tex] p(B) = \frac{2}{3}[/tex]
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:
[tex] P(A|B) = P(A)[/tex]
[tex] P(B|A) = P(B)[/tex]
And for this special case we want to find this probability:
[tex] P(A \cap B)[/tex]
And we can use the following formula:
[tex] P(A \cap B)= P(A)* P(B)[/tex]
And replacing the info we got:
[tex] P(A \cap B) = \frac{5}{7} \frac{2}{3}= \frac{10}{21}=0.476[/tex]
