Mathematics

Problem

Let

A

and

B

be two events defined on the same sample space such that

P(A)=0.4

P(B)=0.5

and

P(A\cap B)=0.20

. a. (i) Verify whether events

A

and

B

are independent. b. (ii) Calculate

P(A\mid B)

and interpret the result in the context of independence. c. (iii) Briefly distinguish between independence and mutual exclusivity, giving one numerical example of mutually exclusive events to support your explanation.

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