# A problem in mathematics is given to three students $\dpi{100} A,B,C$ and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is Option 1) 3/4 Option 2) 1/2 Option 3) 2/3 Option 4) 1/3

As we learnt in

Complementary events -

Let S be the sample space  for a random experiment and let E be the event then complement of event E is

$S-n\left ( E \right )= \left n( E{}' \right )$

$\therefore n\left ( E \right ) + n\left ( E{}' \right )= n\left ( S \right )$

- wherein

where E' contains those element which E does not contain.

$P\bar{(A)}=\frac{1}{2},\ P\bar{(B)}=\frac{2}{3},\ P\bar{(C)}=\frac{3}{4}$

Probability that quostion is not solved=$P\left ( \bar{A} \right ) P\left ( \bar{B} \right ) P\left ( \bar{C} \right )=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}=\frac{1}{4}$

P (question is solved) =$1-P\left ( \bar{A} \right ) P\left ( \bar{B} \right ) P\left ( \bar{C} \right )$

$=1-\frac{1}{4}$

$=\frac{3}{4}$

Option 1)

3/4

Correct option

Option 2)

1/2

Inorrect option

Option 3)

2/3

Inorrect option

Option 4)

1/3

Inorrect option

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