Q76 / 160 · AP EAMCET 2022 (07 Jul Shift 2) · Mathematics

Person $A$ can solve $90 \%$ of the problems given in the book and Person $B$ can solve $70 \%$. Then, the probability that atleast one of them will solve the proplem selected at random from the book is

  • A
    $0.16$
  • B
    $0.69$
  • Correct answer
    C
    $0.97$
  • D
    $0.20$

Solution

Event $A \Rightarrow A$ solves the problem. Event $B \Rightarrow B$ solves the problem. $$ \begin{aligned} \mathrm{P}(\text { success }) & =1-P(\bar{A}) \cdot P(\bar{B}) \\ & =1-\frac{10}{100} \times \frac{30}{100} \\ & =1-\frac{3}{100}=\frac{97}{100}=0.97 \end{aligned} $$

Hence, the correct answer is option: 'C'.

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