A, B, C are three mutually exclusive and exhaustive events of a random experiment. Find the values of P(A), P(B) and P(C), given that
Solution not provided.
Ans. ,
If A and B are two mutually exclusive events, then prove that P(A ∪ B) = P(A) + P(B)
PROOF : Suppose the total number of all possible, mutually exclusive outcomes of an experiment be n
i.e., n(S) = n
Let the outcomes from amongst n possible outcomes, that are favourable to the happening of event A = n(F1) = m1
Also, let the outcomes from amongst n that are favourable to happening of event B = n(F2) = m2
Since event A and event B are mutually exclusive
∴ the number of outcomes that are favourable to the happening of events A or event
By definition,
Hence, when events A and B are mutually exclusive.
(a) From set theory, we know that
...(i)
∴
Since are mutually exclusive.
∴ [By using (i)]
(b) Similarly, we can prove that