Understanding the Problem
To find the probability of selecting a number that is a multiple of both 3 and 4 from the first 50 natural numbers, we first need to determine the total number of favorable outcomes and the total number of possible outcomes.
Total Outcomes
- The total number of natural numbers from 1 to 50 is 50.
Finding Multiples of 3 and 4
- A number is a multiple of both 3 and 4 if it is a multiple of their least common multiple (LCM).
- The LCM of 3 and 4 is 12.
Counting Multiples of 12
- To find how many multiples of 12 are in the range from 1 to 50, we can list them: 12, 24, 36, 48.
- The multiples of 12 within this range are:
- 12 (1 × 12)
- 24 (2 × 12)
- 36 (3 × 12)
- 48 (4 × 12)
- Thus, there are 4 multiples of 12.
Calculating the Probability
- The probability is calculated as the number of favorable outcomes divided by the total number of outcomes:
- Favorable outcomes = 4 (the multiples of 12)
- Total outcomes = 50 (the numbers from 1 to 50)
- Therefore, the probability of selecting a number that is a multiple of both 3 and 4 is:
- Probability = Favorable outcomes / Total outcomes = 4 / 50 = 2 / 25
Final Answer
- The probability that a randomly selected number from the first 50 natural numbers is a multiple of both 3 and 4 is 2/25.