36. 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?
Answer: D
The probability that the number selected will be a prime number or a multiple of 4 is 0.6.
To determine the probability, we first identify the prime numbers and multiples of 4 within the set of integers from 2 to 26. The successful outcomes comprise both prime numbers and multiples of 4, leading to a total of 15 favorable outcomes out of 25 possible integers, resulting in a probability of 0.6.
A) 0.12
This option is incorrect as it does not accurately reflect the number of successful outcomes. The calculation for favorable outcomes leading to this probability is insufficient, as it fails to account for the prime numbers and multiples of 4 correctly.
B) 0.24
Option B is also incorrect. This approximation does not encompass the total number of prime numbers and multiples of 4 within the specified range, resulting in an underestimation of the probability.
C) 0.36
This choice is incorrect as well. The probability of 0.36 suggests a smaller number of successful outcomes than are present in the set of integers from 2 to 26, failing to account for all prime numbers and multiples of 4.
D) 0.6
This option is correct. The total number of prime numbers between 2 and 26 is 9 (2, 3, 5, 7, 11, 13, 17, 19, 23), and the multiples of 4 are 4, 8, 12, 16, 20, 24. Counting the distinct outcomes gives a total of 15 favorable numbers. Thus, the probability calculation of 15/25 simplifies to 0.6.
Conclusion
The correct answer is 0.6 because it accurately represents the combined count of prime numbers and multiples of 4, which totals 15 outcomes. The other options fail because they underestimate the total successful outcomes, leading to inaccurate probability calculations based on the given set of integers.