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 find the probability, we first identify the prime numbers and multiples of 4 within the set of integers from 2 to 26. The prime numbers in this range are 2, 3, 5, 7, 11, 13, 17, 19, 23, and the multiples of 4 are 4, 8, 12, 16, 20, 24. By combining these groups and accounting for any overlap, we find a total of 15 favorable outcomes out of 25 possible selections, leading to a probability of 0.6.

A (0.12) YOUR ANSWER

This choice likely results from an incorrect calculation of the prime numbers or multiples of 4. With only 3 favorable outcomes (for example, 2, 3, and 4), the resulting probability would be 3/25, which is 0.12. However, this does not accurately reflect the total primes and multiples of 4 in the specified range.

B (0.24) YOUR ANSWER

Selecting 6 favorable outcomes could lead to this probability (6/25). However, this figure is too low since it neglects many prime numbers and multiples of 4. It represents a misunderstanding of how many integers in the specified range meet the criteria for being prime or a multiple of 4.

C (0.36) YOUR ANSWER

This option suggests that 9 favorable outcomes were considered (9/25), which is still insufficient. It overlooks several primes and multiples of 4, resulting in a considerably lower probability than the actual count of favorable selections.

D (0.6) CORRECT

This is the correct choice, as it accurately reflects the probability derived from the total of 15 favorable outcomes (10 primes and 6 multiples of 4, minus 1 overlap for 4) out of 25 possible integers, yielding a probability of 0.6.

Conclusion

The probability of selecting either a prime number or a multiple of 4 from the integers 2 to 26 is 0.6, based on the count of distinct integers meeting either criterion. By correctly identifying the primes and multiples within the set, we confirm that the number of favorable outcomes supports this probability calculation. Thus, option D represents the accurate assessment of the situation.

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.

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