Question

A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

Answer 1

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Answer 2

Answer:

The probability that the problem will be solved is 3/4.

Step-by-step explanation:

Given:

The probability that A solves the problem, $P(A)=1 / 2$

The probability that B solves the problem, $P(B)=1/3$

The probability that C solves the problem,$P(C)=1 / 4$

• Hence, By condition of probability

P(A)+P(A')=1

$P\left(A^{\prime}\right)=1 / 2\\P\left(B^{\prime}\right)=2/3\\P\left(C^{\prime}\right)=3 / 4$

The probability that A, B, and C not solving the problem is

$\begin{aligned}&=P\left(A^{\prime}\right) \cdot P\left(B^{\prime}\right) P\left(C^{\prime}\right) \\&=(1 / 2)(2/3)(3 / 4) \\&=1 / 4\end{aligned}$

Hence, the probability that A, B and C solves the problem =$1-(1 / 4)=3 / 4 .$