1.Events X and Y are mutually exclusive.Suppose P(A)=0.30 and P(B)=0.20 .

What is the probability that A or B occurring?

2.Suppose P(A)=0.04 and P(B/A)=0.30.

What is the joint probability of A and B?

1.Events X and Y are mutually exclusive.Suppose P(A)=0.30 and P(B)=0.20 .

What is the probability that A or B occurring?

2.Suppose P(A)=0.04 and P(B/A)=0.30.

What is the joint probability of A and B?

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Here,

P(A) = 0.3

P(B) = 0.2

If events A and B are mutually exclusive, then there is no common element in A and B.

So, A ∩ B = Ø = null set

Therefore, P(A ∩ B) = 0

P(either A or B occurring) = P(A ∪ B)

By addition theorem of probability,

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

= 0.30 + 0.20 - 0

= 0.50

**Hence, the probability that A or B occurring is 0.50**

P(either A or B occurring) = P(A ∪ B)

By addition theorem of probability,

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

= 0.30 + 0.20 - 0

= 0.50

Here,

P(A) = 0.04

P(B/A) = 0.30

We want to find the joint probability of A and B that is P(A ∩ B)=?

We know,

P(B/A) = P(A ∩ B)/P(A)

or P(A ∩ B) = P(A)*P(B/A)

= 0.04*0.30

= 0.12

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