A problem in mathematics is given to 3 students whose chances of solving it are `1/2; 1/3; 1/4`. What is the probability that the problem is solved?

Options

A. `(1)/(12)`
B. `(11)/(12)`
C. `(1)/(2)`
D. `(3)/(4)`

Answer

D

Explanation

`"Let "P(A)=(1)/(2), P(B)=(1)/(3) & P(C)=(1)/(4)`
`P(A cup B cup C)=1-P(overset(_)A)P(overset(_)B)P(overset(_)C)`
`=1-(1-(1)/(2))(1-(1)/(3))(1-(1)/(4))`
`=1-[(1)/(2)xx(2)/(3)xx(3)/(4)]=1-(1)/(3)=(3)/(4)`