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STD 12 - 13. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 13. probability4 Marks
MCQ
Suppose four balls labelled $1,2,3,4$ are randomly placed in boxes $B_1, B_2, B_3, B_4$. The probability that exactly one box is empty is
  • A
    $\frac{8}{256}$
  • ✓
    $\frac{9}{16}$
  • C
    $\frac{27}{256}$
  • D
    $\frac{9}{64}$
✓

Answer

Correct option: B.
$\frac{9}{16}$
b
(b)

Four balls $1,2,3,4$ are randomly placed in boxes $B_1, B_2, B_3, B_4$.

Probability of exactly one box is empty is

$\frac{{ }^4 C_1 \times \frac{4 !}{1 ! \times 2 !} \times \frac{1}{2 !} \times 3 !}{4^4}=\frac{4 \times 6 \times 6}{4 \times 4 \times 4 \times 4}=\frac{9}{16}$

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