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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.
Probability of solving the problem by $A \ B$ is $=1-P\ ($ None of them can solve the problem $)$
$=1-P(\bar{A} \cap \bar{B})=1-P(\bar{A}) \cdot P(\bar{B})$
$=1-[1-P(A)][1-P(B)]$
$=1-\frac{4}{5} \times \frac{3}{5}=\frac{13}{25} .$

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