What is the probability that a positive integer selected at random from the…
2023
What is the probability that a positive integer selected at random from the set of positive integers not exceeding 100 is divisible by either 2 or 5?
- A.
10/5
- B.
3/5
- C.
2/5
- D.
1/5
Attempted by 151 students.
Show answer & explanation
Correct answer: B
Solution:
Count numbers divisible by 2: 50 (2, 4, ..., 100).
Count numbers divisible by 5: 20 (5, 10, ..., 100).
Count numbers divisible by both 2 and 5 (i.e., by 10): 10 (10, 20, ..., 100).
Use inclusion–exclusion to count numbers divisible by 2 or 5: (50 + 20 - 10) = 60 favorable numbers.
Probability = 60/100 = 3/5.
Therefore the correct answer is 3/5.