What is the probability that the number selected is divisible by 4 ?
For the next five (05) items that follow : A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed).
- A. \frac{1}{2}
- B. \frac{7}{16}
- C. \frac{9}{16}
- D. \frac{5}{16} ✓
Correct Answer: D. \frac{5}{16}
Explanation
A number is divisible by 4 if its last two digits are. Possible pairs from {0,1,2,3,4} are 04, 12, 20, 24, 32, 40. Ending in 04, 20, 40 (with zero) gives 3 * (3*2) = 18 ways. Ending in 12, 24, 32 (without zero) gives 3 * (2*2) = 12 ways. Total = 30. Probability = 30/96 = 5/16.
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