Question

A problem in statistics is given to five students A, B, C, and D. Their chances of solving it are $\frac{1}{3}$, $\frac{1}{4}$, $\frac{1}{5}$ and $\frac{1}{6}$ respectively. What is the probability that the problem will be solved?

Answer 1

Probability of A solving $=\frac{1}{3}$

P (A not solving)$=1-\frac{1}{3}$ $=\frac{2}{3}$

Similarly,

P (B not solving) $=1-\frac{1}{4}$ $=\frac{3}{4}$

P (C not solving) $=1-\frac{1}{5}=\frac{4}{5}$

P (D not solving)$=1-\frac{1}{6}=\frac{5}{6}$

Probability of statistics not being solved $=\frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}\times \frac{5}{6}$

$=\frac{1}{3}$

the probability of statistics solved $=1-$Probability of statistics not being solved

Therefore, the probability of statistics solved $=1-\frac{1}{3}$

$=\frac{2}{3}$

Hence the required probability is $\frac{2}{3}$.