First slide

Theorems of probability

Question

A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3, and 1/4. Probability that the problem is solved is

Moderate

A

3/4
B

1/2
C

2/3
D

1/3

Solution

$\begin{array}{l} P (A) = \frac{1}{2}, P (B) = \frac{1}{3}, and P (C) = \frac{1}{4} \\ ∴ P (\bar{A}) = 1 - \frac{1}{2} = \frac{1}{2}, P (\bar{B}) = 1 - \frac{1}{3} = \frac{2}{3} \\ P (\bar{C}) = 1 - \frac{1}{4} = \frac{3}{4} \end{array}$
Therefore, the required probability is
$\begin{matrix} 1 - P (\bar{A}) P (\bar{B}) P (\bar{C}) = 1 - \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \\ = 1 - \frac{1}{4} = \frac{3}{4} \end{matrix}$

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