# Find The Probability of The Problem will be Solved :

A problem in statistics is given to there students A, B and C whose chances of solving it independently are 1/2 , 1/3 and ¼ respectively. The probability that the problem will be solved is

- 1/12
- 11/12
- 1/2
- 3/4

**Answer: (4) 3/4**

**Explanation:-
**

Let A, B, C be the respective events of solving problem and a, b, c be the respective events of not solving the problem. Then A, B, C are independent events.

Therefore, a, b, c are independent events

Then, P (A) = 1/2, P (B) = 1/3 and P (C) = 1/4

and P (a) = 1/2, P (b) = 2/3 and P (c) = 3/4

Therefore, P (none solve the problem) = P (not A) and (not B) and (not C)

= P (a∩b ∩c)

= P (a) P (b) P (c)

= 1 x 2 x 3 /2 x 3 x 4

=1/4

Then, P (the solve the problem) = 1 – 1/4

= (4 – 1)/4

= 3/4

Hence, the answer is (4) 3/4