Question

A can solve 90% of the problems given and B solve 70%. What is the probability of one of them will solve the problem selected from the book?

• A. $\frac{3}{100}$
• B. $\frac{97}{100}$
• C. $\frac{83}{100}$
• D. $\frac{17}{100}$

Answer 1

The correct option is B $\frac{97}{100}$

A : A solves the problem
B : B solves the problem

$P\left(A\right)=\frac{90}{100}\Rightarrow P\left(\overline{A}\right)=1-P\left(A\right)=1-\frac{90}{100}$

$P\left(B\right)=\frac{70}{100}\Rightarrow P\left(\overline{B}\right)=1-P\left(B\right)=1-\frac{70}{100}$

$Requiredprobability=1-P\left(\overline{A}\right)P\left(\overline{B}\right)$