For independent events A_1, A_2, dots, A_n,P( | vedclass

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(C) The probability of non-occurrence of event $A_i$ is given by $P(A_i^c) = 1 - P(A_i) = 1 - \frac{1}{i + 1} = \frac{i}{i + 1}$.Since the events are

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$\frac{1}{n + 1}$

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(C) The probability of non-occurrence of event $A_i$ is given by $P(A_i^c) = 1 - P(A_i) = 1 - \frac{1}{i + 1} = \frac{i}{i + 1}$.Since the events are independent,the probability that none of the events occur is the product of their individual probabilities of non-occurrence:$P(	ext{none occur}) = P(A_1^c) 	imes P(A_2^c) 	imes \dots 	imes P(A_n^c)$$= \left( \frac{1}{2} ight) 	imes \left( \frac{2}{3} ight) 	imes \left( \frac{3}{4} ight) 	imes \dots 	imes \left( \frac{n}{n + 1} ight)$$= \frac{1 	imes 2 	imes 3 	imes \dots 	imes n}{2 	imes 3 	imes 4 	imes \dots 	imes (n + 1)}$$= \frac{1}{n + 1}$.

For independent events $A_1, A_2, \dots, A_n$,$P(A_i) = \frac{1}{i + 1}$ for $i = 1, 2, \dots, n$. Then the probability that none of the events will occur is:

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