Test Index

Probability

Question : 124 of 127

Marks: +1, -0

A, B, C, D

E

\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6} .

Solution:

Concept:

The probability that the problem is solved is the complement of the event that none of the students solves it.

Explanation:

Given probabilities:

P(A)=\frac12

P(B)=\frac13

P(C)=\frac14

P(D)=\frac15

P(E)=\frac16

Assuming independence, probability that none solves =

\left(1-\frac12\right)\left(1-\frac13\right)\left(1-\frac14\right)\left(1-\frac15\right)\left(1-\frac16\right)

Simplify:

\frac12 \times \frac23 \times \frac34 \times \frac45 \times \frac56 = \frac{1}{6}

Thus, probability at least one solves =

1 - \frac16 = \frac56

Answer:

\frac56

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