Given P(A) = 0.9 and P(B) = 0.3, do the following.(a) If A and B are independent events, compute P(A and B).(b) If P(A | B) = 0.6, compute P(A and B).Step 1(a) If A and B are independent events, compute P(A and B).To compute P(A and B) means that we wish to find the probability that both A happened and B happened.Recall that two events are independent if the occurrence or nonoccurrence of one event does not change the probability that the other event will occur.We are given that A and B are independent events, so we can use the multiplication rule for independent events. It is also given that P(A) = 0.9 and P(B) = 0.3.P(A and B)  =  P(A) · P(B) =  (0.9) ·    =

Given P(A) = 0.6 and P(B) = 0.4, do the following.(a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.1, compute P(A and B).

If P(A | B) = 0.6, compute P(A and B).We are given that P(A | B) = 0.6 and P(A) = 0.9. Since P(A | B) ≠ P(A), the occurrence of event B changes the probability that event A will occur. This implies that A and B are events.So, to determine P(A and B), we can apply the general multiplication rule for events. Recall that P(B) = 0.3.P(A and B)  =  P(B) · P(A | B) =  (0.3) ·    =

Given P(A) = 0.3, P(B) = 0.5, P(A | B) = 0.3, do the following.(a) Compute P(A and B).(b) Compute P(A or B).Step 1(a) Compute P(A and B).To compute P(A and B) means that we wish to find the probability that both A happened and B happened. We are given that P(A) = 0.3, P(B) = 0.5, and P(A | B) = 0.3.Since P(A | B) ≠ P(A), the occurrence of event B the probability that event A will occur. This implies that A and B are not independent events.So, to determine P(A and B), we can apply the general multiplication rule for events.P(A and B)  =  P(B) · P(A | B) =  (0.5) ·    =

Suppose that the probability of event A is 0.2 and the probability of event B is 0.4. Also, suppose that the two events are independent. Then P(A|B) is:Question 16Select one:a.P(A)/P(B) = 0.2/0.4 = ½b.None of the above.c.P(A) = 0.2d.P(A) × P(B) = (0.2)(0.4) = 0.08

If the probability of Event A occurring is 0.6, and the probability of Event B occurring is 0.4, what is the probability of both events happening together, assuming they are independent?a.0.24b.0.1c.0.06d.0.16