A problem in Mathematics is given to three students  A, B, C and their respective probability of solving  the problem are 12,13 and 14. Probability that the problem is solved, is

# A problem in Mathematics is given to three students  and their respective probability of solving  the problem are and $\frac{1}{4}$. Probability that the problem is solved, is

1. A

$\frac{3}{4}$

2. B

$\frac{1}{2}$

3. C

$\frac{2}{3}$

4. D

$\frac{1}{3}$

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### Solution:

Consider the following events:

= Student solves the problem

= Student solves the problem

= Student solves the problem

Clearly, $E,F,G$ are independent events such that

$P\left(E\right)=\frac{1}{2},P\left(F\right)=\frac{1}{3}$ and $P\left(G\right)=\frac{1}{4}$

Required probability  $=P\left(E\cup F\cup G\right)$

Required probability = $1-P\left(\overline{E}\right)P\left(\overline{F}\right)P\left(\overline{G}\right)$

Required probability = $=1-\frac{1}{2}×\frac{2}{3}×\frac{3}{4}=\frac{3}{4}$  Register to Get Free Mock Test and Study Material

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