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16 Sep 2014, 01:16
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If two integers are selected, one after the other with replacement, from a set of integers from 20 to 29, inclusive, what is the probability that one of the selected integers is a prime number, and the other is a multiple of 3?
A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20
A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20
16 Sep 2014, 01:16
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Official Solution:
If two integers are selected, one after the other with replacement, from a set of integers from 20 to 29, inclusive, what is the probability that one of the selected integers is a prime number, and the other is a multiple of 3?
A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20
Start by identifying the prime integers and multiples of 3 in the range 20 to 29. The prime integers are 23 and 29, while the multiples of 3 are 21, 24, and 27.
We can then consider two cases:
Case 1: The first number selected is prime, and the second is a multiple of 3. The probability of this is (2/10) * (3/10) = 0.06. Notice, that since we are selecting two integers with replacement, the denominator for selection case is 10 (the total number of integers in the given range).
Case 2: The first number selected is a multiple of 3, and the second is prime. The probability of this is (3/10) * (2/10) = 0.06.
Therefore, the total probability is the sum of the probabilities of the above two cases: 0.06 + 0.06 = 0.12.
Answer: B
If two integers are selected, one after the other with replacement, from a set of integers from 20 to 29, inclusive, what is the probability that one of the selected integers is a prime number, and the other is a multiple of 3?
A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20
Start by identifying the prime integers and multiples of 3 in the range 20 to 29. The prime integers are 23 and 29, while the multiples of 3 are 21, 24, and 27.
We can then consider two cases:
Case 1: The first number selected is prime, and the second is a multiple of 3. The probability of this is (2/10) * (3/10) = 0.06. Notice, that since we are selecting two integers with replacement, the denominator for selection case is 10 (the total number of integers in the given range).
Case 2: The first number selected is a multiple of 3, and the second is prime. The probability of this is (3/10) * (2/10) = 0.06.
Therefore, the total probability is the sum of the probabilities of the above two cases: 0.06 + 0.06 = 0.12.
Answer: B
30 Mar 2023, 10:01
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
