Identifying Multiples of 3
The set of numbers is S = {1, 2, ..., 50}. The total count of numbers in the set is 50.
We need to find the numbers in S that are divisible by 3.
- The count of numbers divisible by 3 is calculated as $\lfloor \frac{50}{3} \rfloor = 16$.
Calculating Probability
The question concerns the probability that the product $ab$ of two distinct numbers selected from S is divisible by 3. The provided answer suggests focusing on the proportion of numbers divisible by 3 in the set.
Consider the probability of selecting a single number from the set S that is divisible by 3:
$ P(\text{Number divisible by 3}) = \frac{\text{Count of numbers divisible by 3}}{\text{Total numbers in the set}} $
Substituting the values:
$ P(\text{Number divisible by 3}) = \frac{16}{50} $
Simplifying the fraction:
$ \frac{16}{50} = \frac{8}{25} $
This resulting probability matches the required outcome.
Similar Questions
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Important Questions from Arithmetic
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