Question

A problem in mathematics is given to 4 students whose chances of solving individually are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}. $ probability that the problem will be solved at least by one student is

• A. $\frac{2}{3}$
• B. $\frac{3}{5}$
• C. $\frac{4}{5}$
• D. $\frac{3}{4}$

Answer 1

Answer: (C)

$P\left(A \cup B \cup C \cup D\right) = 1 -P\left(A^{c} \cap B^{c} \cap C^{c} \cap D^{c}\right)$
$= 1-P\left(A^{c}\right)\cdot P\left(B^{c}\right)\cdot P\left(C^{c}\right)\cdot P\left(D^{c}\right)$
$=1-\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}$
$=1-\frac{1}{5} = \frac{4}{5}$