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Model Paper 5 — Applied Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsModel Paper 51 Mark
MCQ
Two men hit at a target with probabilities $\frac{1}{2}$ and $\frac{1}{3}$, respectively. What is the probability that exactly one of them hits the target?
  • A
    $\frac{1}{6}$
  • B
    $\frac{1}{2}$
  • C
    $\frac{1}{3}$
  • D
    $\frac{2}{3}$
✓

Answer

(b) $\frac{1}{2}$
Explanation: Let A be the event that Mr. A hit the target and B be the event that Mr. B hit the target
$\therefore \mathrm{P}(\mathrm{A})=\frac{1}{2}$ and $\mathrm{P}(\mathrm{B})=\frac{1}{3}$
Now, P (exactly one of them hits the target)
$=\mathrm{P}(\mathrm{A} \cap \bar{B}$ or $\bar{A} \cap \mathrm{~B})$
$=\mathrm{P}(\mathrm{A} \cap \bar{B})+\mathrm{P}(\bar{A} \cap \mathrm{~B})$
$=\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\bar{B})+\mathrm{P}(\bar{A}) \cdot \mathrm{P}(\mathrm{B})$
$=\frac{1}{2} \cdot \frac{2}{3}+\frac{1}{2} \cdot \frac{1}{3}=\frac{3}{6}=\frac{1}{2}$

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