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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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:

Similar Questions

$A$ coin and a six-faced die,both unbiased,are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is:

$A$ coin is tossed three times. Let $A$ be the event of "getting three heads" and $B$ be the event of "getting a head on the first toss". Then $A$ and $B$ are

When three coins are tossed simultaneously,what is the probability of getting a head on the first,a tail on the second,and a head on the third?

$A$ coin is tossed and a die is thrown. The probability that the outcome will be a head or a number greater than $4$ or both,is

Three coins are tossed once. Find the probability of getting exactly $2$ tails.

Vedclass Test Series

Exam Paper Generator

Online Exam Module