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14.Probability
hard
A problem in Mathematics is given to three students $A, B, C$ and their respective probability of solving the problem is $\frac{1}{2} , \frac{1}{3} $ and $\frac{1}{4}$. Probability that the problem is solved is
A
$\frac{3}{4}$
B
$\frac{1}{2}$
C
$\frac{2}{3}$
D
$\frac{1}{3}$
(AIEEE-2002)
Solution
(a) Probability problem is not solved by $A = \,1 – \frac{1}{2} = \frac{1}{2}$
Probability problem is not solved by $B = 1 – \frac{1}{3} = \frac{2}{3}$
Probability problem is not solved by $C = 1 – \frac{1}{4} = \frac{3}{4}$
Probability of solving the problem $ = 1 – P$ (not solved by any body)
$\therefore$ $P = 1 – \frac{1}{2}.\,\,\frac{2}{3}.\,\frac{3}{4}\, = \,1 – \frac{1}{4} = \frac{3}{4}$.
Standard 11
Mathematics
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