Events are independent?

Probability Level 2

Let E 1 , E 2 , E 3 , . . . . , E n E_1,E_2,E_3,....,E_n be n n independent events such that P ( E i ) = 1 i + 1 P(E_i)=\dfrac{1}{i+1} for i = 1 , 2 , 3 , . . . , n . i=1,2,3,...,n. What will be the probability that at least one of the events occurs ?

Note : P ( A ) P(A) denotes the probability of occurrence of event A . A.

1 n + 1 \frac{1}{n+1} n n + 1 \frac{n}{n+1} 1 − 1 n 1-\frac{1}{n} 1 n \frac{1}{n}

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Daniel Liu
Jan 29, 2015

Instead we find the probability that none of the events happen.

this happens with probability 1 2 ⋅ 2 3 ⋯ n − 1 n ⋅ n n + 1 = 1 n + 1 \dfrac{1}{2}\cdot \dfrac{2}{3}\cdots \dfrac{n-1}{n}\cdot \dfrac{n}{n+1}=\dfrac{1}{n+1}

thus the probability of at least one event happening is 1 − 1 n + 1 = n n + 1 1-\dfrac{1}{n+1}=\boxed{\dfrac{n}{n+1}}

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Used the same method .

A Former Brilliant Member - 6 years, 4 months ago

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