Question

X can solve 80% of the problems while Y can solve 90%of the problems given in a statistics book. A problem is selected at random. What is the probability that at least one of them will solve the problem.

• A. 0.95
• B. 0.98
• C. 0.96
• D. 0.99

Answer 1

The correct option is B 0.98

$Let{E}_1,E_{2}eventso\text{f solving a problem by A and B respectively}$
$\text{Way in which atleast one of them solve the problem:}$
$\text{i)A solves and B fails}$
$\text{ii)A fails and B solve}$
$\text{iii) A and B solve the problem}$
$\text{Required probability=}\frac{80}{100}\times \frac{10}{100}+\frac{20}{100}\times \frac{90}{100}+\frac{80}{100}\times \frac{90}{100}$
$=\frac{8}{100}+\frac{18}{100}+\frac{72}{100}$
$=\frac{98}{100}=0.98$