Question

Please I need a step by step approach to these problem. Thank you

Step 1

(a) Let us assume that P(A), P(B) > 0.

We know P(A|B) = P(A∩B)/P(B).----------------(1)

We need to show that P(A|B) + P(A^{c}|B) = 1

From the fig below, it can be seen that,

B = (A∩B)∪( A^{c}∩B )

=> P(B) = P(A∩B) + P(A^{c}∩B)

=>P(A∩B)/P(B) + P(A^{c}∩B)/P(B) = 1

Step 2

So, &n...

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