Question

Three students try to solve a problem independently with a probability of solving it as $\frac{1}{3},\frac{2}{5},\frac{5}{12}$ respectively. What is the probability that the problem is solved?

• A. $\frac{1}{18}$
• B. $\frac{12}{30}$
• C. $\frac{23}{30}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{23}{30}$

The probability that the problem is solved by 1st, 2nd and 3rd student is $\frac{1}{3},\frac{2}{5},\frac{5}{12}$ respectively.

The probability that problem is not solved by 1st student $=1-\frac{1}{3}=\frac{2}{3}$

The probability that problem is not solved by 2nd student $=1-\frac{2}{5}=\frac{3}{5}$

The probability that problem is not solved by 3rd student $=1-\frac{5}{12}=\frac{7}{12}$

Thus, the probability that no one will solve the problem $=\frac{2}{3}\times \frac{3}{5}\times \frac{7}{12}=\frac{7}{30}$

Thus, the probability that problem is solved $=1-\frac{7}{30}=\frac{23}{30}$