What is the probability that a number picked at random from the first 50 natural numbers is composite__________?
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Answer: B. 17/25
Explanation
Among the first fifty natural numbers, exactly one number is neither prime nor composite. Counting the fifteen prime numbers leaves thirty four composite numbers in the specified range. Dividing thirty four by fifty and simplifying the fraction gives seventeen over twenty five. A composite number is a positive integer greater than one that has positive divisors other than one and itself. Prime numbers possess exactly two distinct positive divisors which are one and the number itself. Probability is calculated by dividing the number of favorable outcomes by the total possible outcomes.
Number theory applications in cryptography rely heavily on distinguishing prime numbers from composite integers. Random sampling algorithms evaluate number properties to test statistical distribution uniformity. Educational software uses basic probability problems to teach students fundamental counting principles. Option a assumes twenty one favorable outcomes which miscounts the total number of composite integers. Option c represents the probability of picking a prime number rather than a composite number. Option d corresponds to an incorrect count of composite numbers within the first fifty integers.
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