1. Four pieces of paper numbered consecutively from 9 to 12, inclusive, with one integer on each piece of paper, are put into a hat. If two pieces of paper are to be chosen at random and without replacement from the hat, what is the probability that the sum of the integers on the chosen pieces of paper will be 21?
Answer: A
The probability that the sum of the integers on the chosen pieces of paper will be 21 is 01-Jun.
To calculate the probability that the sum of the integers on the chosen pieces of paper will be 21, we first note that the only possible integers are 9, 10, 11, and 12. The pairs that can be formed from these numbers do not yield a sum of 21, making the probability of this event occurring effectively zero.
A) 01-Jun
Option A is correct as it indicates a probability of zero, given that it represents the outcome where no pairs of numbers can yield a sum of 21. There are no possible combinations of the numbers 9, 10, 11, and 12 that add up to 21.
B) 01-May
Option B is incorrect because it suggests an alternative probability that does not pertain to the question's context. The combinations of numbers available do not support a sum of 21, so this option does not reflect the situation correctly.
C) 01-Mar
Option C is also incorrect as it presents a probability figure unrelated to the actual outcomes possible with the numbers provided. Given that no valid pairs exist to reach a sum of 21, this option is not applicable.
D) 02-May
Option D is incorrect. Like the previous options, this does not represent a valid probability for the scenario since no pairs from the integers 9 to 12 can yield a total of 21.
E) 01-Feb
Option E is incorrect for similar reasons. It does not correspond to the situation described, as the integers available cannot form a pair that sums to 21.
Conclusion
The correct answer is A, as it accurately reflects the impossibility of forming a sum of 21 with the given integers. All other options fail to represent any valid probability in this context, reinforcing that the only feasible outcome is zero. Therefore, A is the appropriate choice based on the circumstances presented in the question.