Question

P(A) = .6, P(B) = .3, P(B | A) = .5

Answer 1

P(A and B) =

A. .06
B. .30
C. .03
D. .18
E. .05

Answer 2

Is this 18 or 0.18?

Answer 3

0.18

Answer 4

Is there any other data for this question?

Answer 5

No, just that one at the top

Answer 6

\[P(B|A)=\frac{P(A\text{ and }B)}{P(A)}\]
then

\[P(A\text{ and }B)=P(B|A)P(A)\]

Answer 7

So at first, it would be,
\[P(B|A) = \frac{ .9 }{ .6 }\] ? Or did I do that wrong?

Answer 8

Here is a method to solve it;
Probability that A occurs is P(A)=.6
Probability that B occurs is P(B)=.3
Probability that event A does not occur, P(A')=0.4
Probability that event B does not occur, P(B')=0.7
Probability that event A and event B both occur, P(A∩B)=0.18

Answer 9

\[P(A\text{ and }B)=P(B|A)P(A)=.5\times.6\]

Answer 10

Ah, I see. The solution would be .30?

Answer 11

yes

Answer 12

Thank you so much!