Let a and b be two disjoint events with pa 034 and pb 038...

- Let a and b be two disjoint events with P(a) = 0.34 and P(b) = 0.38. What is P(A and B)? - Let a and b be two independent events with P(a) = 0.18 and P(b) = 0.74. What is P(A and B)? - Let a and b be two disjoint events such that P(a) = 0.24 and P(b) = 0.44. What is P(a or b)? - Let a and b be two independent events. If P(A) = 0.71 and P(B) = 0.22, what is P(A | B)?

Transcript

00:01 All right, so in this problem, we are focusing on two events that are either disjoint or independent.

00:09 And we'll kind of go through those different outcomes.

00:14 So the first option that says let a and b be two disjoint events with the probability of a being 0 .34 and the probability of b being 0 .38.

00:30 Now the reason why my venn diagram is not touching is because disjoint, also known as mutually exclusive, means that they cannot occur at the same time.

00:45 There is no overlap.

00:47 So then, i mean, if we wanted to find the probability of not a or b, we could do 1 minus 0 .34 minus 0 .38.

00:55 And that gives us 0 .28.

00:58 All right.

00:58 So that first question, it says, what is the probability of a and b? that is zero because they're a disjoint.

01:08 There's no overlap between the two circles.

01:12 So that is our kind of our first thing there, first little option there.

01:18 So the second thing that it gives us is independence.

01:23 Independence means that the two events are not affecting each other.

01:28 They are occurring independent of each other.

01:32 And when two events are independent, we can find the probability of a and b.

01:38 By taking the probability of a and multiplying it by the probability of b.