Given that pa 035 pb 045 and pa b 013 a find pa b 2 b...

Given that P(A) = 0.35, P(B) = 0.45, and P(A ∩ B) = 0.13, (a) Find P(A' | B'), (2) (b) Explain why the events A and B are not independent. The event C has P(C) = 0.20. The events A and C are mutually exclusive, and the events B and C are statistically independent. (c) Draw a Venn diagram to illustrate the events A, B, and C, giving the probabilities for each region. (5) (d) Find P([B ∪ C]' ) (2)

Transcript

0:00 Hello everyone.

00:01 So in this question the given information are probability of a is equal to 0 .35 probability of b is equal to 0 .45 and probability of a intersection b is 0 .13.

00:23 So the first which we have to calculate is probability of a given b.

00:29 So this is same as probability of a intersection b divided by probability of b substituting the values 0 .13 divided by 0 .45 which is equals to 0 .29.

00:47 Part second is we have to tell our in a and b events independent.

00:54 So for two events to be independent, the condition is if a and b are independent, then probability of a given b should be equal to probability of a.

01:22 But here, but probability of a given b, which is equal to 0 .29 is not equals to 0 .35 which is the probability of b.

01:36 A.

01:38 Thus we will say that these two events are not dependent, not independent.

01:54 The next information given is if probability of c is equal to the probability of c is equal to, to 0 .20, also it is given that if a and c are mutually exclusive, that is for two events to be mutually exclusive, the intersection is zero, they are disjoint.

02:11 So probability of a intersection c is equals to 0.

02:14 Also it is given that b and c are independent events, that is probability of b intersection c becomes probability of b multiplied by probability of c substituting the values probability of b is 0 .45 multiplied by probability of c 0 .20 which is equal to 0 .09.

02:40 We have to make the vein diagrams for events a, b and c.

02:45 So the first condition is a and c are disjoint.

02:49 So say this is a a and this becomes our c, a, next is given that b is in, okay, so next it is given that there b and c are not disjoint also because b intersection, probability of b intersection c is not equals to zero, so b and c are not disjoint...

Question

Please give Ace some feedback