If A and B be two independent events then show that A, B' are also independent.

Engineering

Mathematics

Conditional Probability

Question

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Given A and B are independent events.

Then P(A∩B) = P(A)⋅P(B).......(1).

Now,

P(A∩B')

= P(A) – P(A∩B) [ From the definition of (A∩B')]

= P(A) – P(A)⋅P(B) [ Using (1)]

= P(A){1 – P(B)}

= P(A)⋅P(B').

So P(A∩B') = P(A)⋅P(B').

This gives A, B' are independent.

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