JUST STEP 2 PART B

ivenP(A) =0.5

andP(B) =0.7,

do the following.

(a) IfAandBare independent events, computeP(AandB).

(b) IfP(A|B) =0.8,

computeP(AandB).

Step 1

(a) IfAandBare independent events, computeP(AandB).

To computeP(AandB)

means that we wish to find the probability that bothAhappened andBhappened.

Recall that two events are independent if the occurrence or nonoccurrence of one event doesnotchange the probability that the other event will occur.

We are given thatAandBare independent events, so we can use the multiplication rule for independent events. It is also given thatP(A) =0.5

andP(B) =0.7.

P(AandB)=P(A)P(B)

=(0.5).35

0.7

=.56

0.35

Step 2

(b) IfP(A|B) =0.8,

computeP(AandB).

We are given thatP(A|B) =0.8

andP(A) =0.5.

SinceP(A|B)P(A),

the occurrence of eventBchanges the probability thateventAwill occur. This implies thatAandBare

---Select---

independent

not independent

events.

So, to determineP(AandB),

we can apply the general multiplication rule for events. Recall thatP(B) =0.7.

P(AandB)=P(B)P(A|B)

=(0.7)

=