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Probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSProbability1 Mark
MCQ
Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is:
  • A
    $\frac{1}{5}$
  • B
    $\frac{4}{5}$
  • C
    $\frac{1}{30}$
  • ✓
    $\frac{5}{9}$
✓

Answer

Correct option: D.
$\frac{5}{9}$
The given digits are 0, 2, 3 and 5.
_____ _____ _____ _____
Thousands Hundreds Tens Ones
Now, there are 3 ways to fill the thousands place (0 cannot occupy the thousands place), 3 ways to fill the hundreds place, 2 ways to fill the tens place and 1 way to fill the ones place. Total number of four digit numbers formed = 3 × 3 × 2 × 1 = 18 We know that a number is divisible by 5 if it ends in 0 or 5. When 0 is at the ones place, Number of four digits numbers divisible by 5 formed = 3 × 2 × 1 = 6 When 5 is at the ones place, Number of four digits numbers divisible by 5 formed = 2 × 2 × 1 = 4 (0 cannot occupy the thousands place) Total number of four digit numbers divisible by 5 = 6 + 4 = 10 $\therefore$ P(four digit number formed is divisible by 5) $=\frac{\text{Total Number of four digit numbers divisible by 5}}{\text{Total Number of w4 digit numbers formed}}$ $=\frac{10}{18}=\frac{5}{9}$ Hence, the correct answer is option (d).

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