What is the probability that the number selected is divisible by 2 ?
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{5}{8} ✓
- B. \frac{3}{8}
- C. \frac{1}{8}
- D. \frac{5}{24}
Correct Answer: A. \frac{5}{8}
Explanation
Total 4-digit numbers without repetition from {0,1,2,3,4} is 4 * 4 * 3 * 2 = 96. A number is divisible by 2 if it ends in 0, 2, or 4. Cases ending in 0: 4*3*2 = 24. Cases ending in 2: 3*3*2 = 18. Cases ending in 4: 3*3*2 = 18. Total favorable cases = 24 + 18 + 18 = 60. Probability = 60/96 = 5/8.
Related questions on Statistics & Probability
- Let x be the mean of squares of first n natural numbers and y be the square of mean of first n natural numbers. If $\frac{x}{y}=\fra...
- What is the probability of getting a composite number in the list of natural numbers from 1 to 50?
- Two numbers x and y are chosen at random from a set of first 10 natural numbers. What is the probability that (x+y) is divisible by 4?
- A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies $x+\frac{1}{x} \gt...
- Three fair dice are tossed once. What is the probability that they show different numbers that are in AP?