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Probability — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsProbability1 Mark
MCQ
A number was chosen at random from first 300 three-digit natural numbers. The probability that the selected number has zero at units place is
  • A
    $\frac{1}{15}$
  • B
    $\frac{1}{25}$
  • ✓
    $\frac{1}{10}$
  • D
    $\frac{1}{20}$
✓

Answer

Correct option: C.
$\frac{1}{10}$
(c) First 300 three digit numbers are: 100, 101, ..., 399. Out of these one number can be chosen in 300 ways.
∴ Total number of elementary events = 300
A number having 0 at unit's place is divisible by 10. Such numbers are 100, 110, 120, ..., 390. These numbers form an AP with common difference 10. Let there number be n. Then, $390=100+(n-1) \times 10 \Rightarrow 290=10(n-1) \Rightarrow n=30$.
∴ Favourable number of elementary events = 30.
Hence, required probability $=\frac{30}{300}=\frac{1}{10}$.

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