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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
Assertion (A) : The probability that candidates $A$ and $B$ can solve the problem is $\frac{1}{5}$ and $\frac{2}{5}$, then probability that problem will be solved is given by $\frac{12}{25}$.
Reason (R): If events $A \& B$ are independent, then $P(A \cap B)=P(A) \times P(B)$.
  • A
    Both (A) and (R) are true and (R) is the correct explanation of (A).
  • B
    Both (A) and (R) are true but (R) is not the correct explanation of (A).
  • C
    (A) is true but (R) is false.
  • ✓
    (A) is false but (R) is true.
✓

Answer

Correct option: D.
(A) is false but (R) is true.
(d) : Probability of solving the problem by $A \& B$ is $=1-P($ None of them can solve the problem $)$
$
\begin{array}{l}
=1-P(\bar{A} \cap \bar{B})=1-P(\bar{A}) \cdot P(\bar{B}) \\
=1-[1-P(A)][1-P(B)]=1-\frac{4}{5} \times \frac{3}{5}=\frac{13}{25} .
\end{array}
$

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