9.) (10) The Venn diagram below represents probabilities for...

9.) (10) The Venn diagram below represents probabilities for events A and B. Determine each probability. (a) P(A AND B) (b) P(A OR B) (c) P(NOT A AND NOT B) (d) P(A|B) (e) P(B|A) 0.23 0.43 0.11 0.23 A B

Transcript

00:01 And asked a question given a venn diagram to represent probabilities for events a and b and it's required to determine each of the following probabilities let's start by the vendagram it's a given here we have event a intersected with event b and this area or this portion as a probability of 0 .43 is for a and this is for b and the probability of the intersection section is 0 .11 and here we have 0 .23 as here is 0 .23.

00:45 For part a it's required to find the probability of a and b.

00:53 This is the probability of the intersection.

00:55 A and b means the probability of a intersect b and this is directly given.

01:04 It is 0 .11.

01:07 For part b, it's required to find the probability of a or b that is the probability of a only or the probability of b only or the probability of both that is 0 .43 plus the probability of b only 0 .23 plus which is 0 .11 which equals 0 .7 7 let's move to bar c the probability of node a and node b which is a complement and b complement or in terms of intersections it's a probability of a complement intersect b complement here we have two ways to answer this problem one way is to use the venn diagram directory another way is to use the morgan's law if we used the vendagram directly what is a complement it is everything except a then we have these area and what does it mean intersect with b complement that is the intersection with everything except b and this is a shaded area what is the probability of the shaded area is 0 .23 for part d it's a probability of a given b again we can use venn diagram direct or use the conditional probability rule.

03:17 What does it mean probability of a given b? we are conditioning on b.

03:23 Imagine that this is the only space that we have.

03:29 What is the probability of a now? the reality of a is just this area because it contains a with respect to the total area of b.

03:42 Then it is 0 .11 divided by 0 .11 plus 0 .23...

Question

9.) (10) The Venn diagram below represents probabilities for events A and B. Determine each probability. (a) P(A AND B) (b) P(A OR B) (c) P(NOT A AND NOT B) (d) P(A|B) (e) P(B|A) 0.23 0.43 0.11 0.23 A B

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