Multiple choice

A number is selected at random from the first twenty-five natural numbers. If it is a composite number then it is divided by 5. But if it is not a composite number, it is divided by 2. The probability that there will be no remainder in division is

  1. $\displaystyle \frac{11}{30}$
  2. $.0.4$
  3. $0.2$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Numbers 1-25. Composite: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25 (15 total). Non-composite: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23 (10 total). Composite divisible by 5: 10, 15, 20, 25 (4). Non-composite divisible by 2: 2 (1). Total favorable = 5. Probability = 5/25 = 0.2.

AI explanation

From the first twenty-five natural numbers, the composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, and 25, totaling 15 numbers where 25, 20, 15, and 10 are divisible by 5. The non-composite numbers (1 and the primes) total 10 numbers, but only 2 yields no remainder when divided by 2, making the total successful outcomes 5. The probability is 5 successful outcomes out of 25 total numbers, which equals 0.2.

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