A number is to be selected at random from the set of 25 integers from 2 to 26. What is the probability that the number selected will be a prime number or a multiple of 4?

Rationale

The probability that the number selected will be a prime number or a multiple of 4 is 0.6.

To determine this probability, we first identify the prime numbers and the multiples of 4 within the set of integers from 2 to 26. The primes in this range are 2, 3, 5, 7, 11, 13, 17, 19, 23, totaling 9 primes. The multiples of 4 are 4, 8, 12, 16, 20, 24, totaling 6 multiples. However, the number 12 is counted in both categories, so we use the principle of inclusion-exclusion to find the combined total.

A (0.12) YOUR ANSWER

This probability suggests that only a few numbers qualify as either prime or multiples of 4. However, given the counts of 9 primes and 6 multiples of 4, this value is too low and fails to account for the overlap, leading to an inaccurate total.

B (0.24) YOUR ANSWER

While this option acknowledges the existence of both primes and multiples of 4, it still underestimates the total count of qualifying numbers. With a total of 15 unique numbers (9 primes + 6 multiples - 1 overlap), this probability does not reflect the actual proportions.

C (0.36) YOUR ANSWER

Although closer to the correct probability, this value still falls short. It suggests that only a fraction of the total integers are either prime or multiples of 4, overlooking the significant number of primes and the correct inclusion of the overlaps.

D (0.6) CORRECT

This is the correct answer as it accurately represents the ratio of favorable outcomes to the total possible outcomes. There are 15 qualifying numbers (9 primes + 6 multiples - 1 overlap) out of 25 total integers, leading to a probability of 15/25 = 0.6.

Conclusion

In conclusion, the probability that a randomly selected number from the set of integers from 2 to 26 is either a prime number or a multiple of 4 is 0.6. This calculation effectively combines the counts of unique primes and multiples, aligning with the principles of probability and inclusion-exclusion to arrive at the correct result.

A number is to be selected at random from the set of 25 integers from 2 to 26. What is the probability that the number selected will be a prime number or a multiple of 4?

The probability that the number selected will be a prime number or a multiple of 4 is 0.6.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test