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 `3//4` b. `1//2` c. `2//3` d. `1//3`

Options

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

Answer

A

Explanation

consider the following events :
E=Student A solves the problem
F=Student B solves the problem
G=Student C solves the problem
Clearly, E, F, G are independent events such that
`P(E )=(1)/(2), P(F)=(1)/(3) " and " P(G)=(1)/(4)`
Required probability `=P(E cup F cup G)`
`implies` Required probability `=1-P(overline(E )) P(overline(F)) P(overline(G))`
`implies` Required probability `=1-(1)/(2)xx(2)/(3)xx(3)/(4)=(3)/(4)`