Q.154. Probability

Question 154.
Let A sub 1,A sub 2, .........A sub n be independent events. Let P(A sub i)= 1/(i+1) for i= 1,2,....n. Find the probability that none of the events occurs.

Answer 154.
For A' compliment of A,
P(A sub i)= 1/(i+1)
=> P(A' sub i) = 1 - 1/(1 +i) = i / (1 +i)
Probability that none of the events occurs
= P[(A' sub 1) ∩ (A' sub 2) ∩ ... ∩ (A' sub n)]
= P(A' sub 1) * P(A' sub 2) * ... * P(A' sub n)
= [1 / (1 + 1)] * [2 / (2 + 1)] * [3 / (3 + 1)] * .... * [n / (n + 1)]
= 1 / (n + 1).

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