The probability of success of three students Karan- Sarosh and Vignesh in the one examination are 1-5- 1-4 and 1-3 respectively- What is the probability that at least two of them will be successful-

The correct option is E None of these A – Karan B – Sarosh C – Vignesh P(A) = 1/5 , P(B) = 1/4 , P(C) = 1/3 ∴ Required probability = [P(A)P(B)1−P(C)] + [1−P(A) ...

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Question

The probability of success of three students Karan, Sarosh and Vignesh in the one examination are $\frac{1}{5}$ , $\frac{1}{4}$ and $\frac{1}{3}$ respectively.
What is the probability that at least two of them will be successful?

$\frac{1}{6}$

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$\frac{2}{5}$

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$\frac{3}{5}$

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$\frac{3}{5}$

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None of these

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Solution

The correct option is E
None of these

A – Karan

B – Sarosh

C – Vignesh

P(A) = $\frac{1}{5}$ , P(B) = $\frac{1}{4}$ , P(C) = $\frac{1}{3}$

$∴$ Required probability = [P(A)P(B){1−P(C)}] + [{1−P(A)}P(B)P(C)] + [P(A)P(C){1−P(B)}] + P(A)P(B)P(C) = $\frac{9}{60}$

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The probability of success of three students Karan, Sarosh and Vignesh in the one examination are 15, 14 and 13 respectively. What is the probability that at least two of them will be successful?

The correct option is E None of these A – Karan B – Sarosh C – Vignesh P(A) = 15 , P(B) = 14 , P(C) = 13 ∴ Required probability = [P(A)P(B){1−P(C)}] + [{1−P(A)}P(B)P(C)] + [P(A)P(C){1−P(B)}] + P(A)P(B)P(C) = 960

The probability of success of three students Karan, Sarosh and Vignesh in the one examination are $\frac{1}{5}$ , $\frac{1}{4}$ and $\frac{1}{3}$ respectively.
What is the probability that at least two of them will be successful?

The correct option is E
None of these

A – Karan

B – Sarosh

C – Vignesh

P(A) = $\frac{1}{5}$ , P(B) = $\frac{1}{4}$ , P(C) = $\frac{1}{3}$

$∴$ Required probability = [P(A)P(B){1−P(C)}] + [{1−P(A)}P(B)P(C)] + [P(A)P(C){1−P(B)}] + P(A)P(B)P(C) = $\frac{9}{60}$