Question

A can solve 75% of the problems of Mathematics and B can solve 70%. What is the probability that either A or B can solve a problem chosen at random ?

• A. $\frac{3}{40}$
• B. $\frac{21}{40}$
• C. $\frac{37}{40}$
• D. $\frac{19}{40}$

Answer 1

Answer: (C)

$\frac{37}{40}$

Given $P\left(A\right)=\frac{75}{100}=\frac{3}{4}$
$P\left(B\right)=\frac{70}{100}=\frac{7}{10}$
Clearly , A and B are independent events
Now, $P(A\cup B)=1-P\left(\overline{A\cup B}\right)$
$=1-P(\overline{A}\cap \overline{B})$
$=1-P\left(\overline{A}\right)P\left(\overline{B}\right)$ (Since, A and B are independent events , so $\overline{A},\overline{B}$ are also independent.)
$=1-(1-\frac{3}{4})(1-\frac{7}{10})$
$\Rightarrow P(A\cup B)=\frac{37}{40}$