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?

Rationale

The probability that the sum of the integers on the chosen pieces of paper will be 21 is 01-Jun.

To achieve a sum of 21 using the integers 9, 10, 11, and 12, the only possible combination is 10 and 11, which sums to 21. However, since the total number of combinations possible when selecting two pieces of paper from four is six, the probability of choosing the specific combination that sums to 21 is 1 out of 6.

A (01-Jun) CORRECT

This choice represents the correct probability. The only pair of numbers among the selections that can sum to 21 is 10 and 11, which occurs once among the total combinations of selecting any two pieces of paper from the four available.

B (01-May) YOUR ANSWER

This choice is incorrect because it suggests a probability of 1 out of 5. However, the correct total number of ways to select two papers from four is 6, not 5, making this choice an inaccurate representation of the calculated probability.

C (01-Mar) YOUR ANSWER

This option indicates a probability of 1 out of 3, which is also incorrect. The actual combinations possible from four papers must be accounted for, and with only 6 combinations available, this choice does not reflect the correct probability.

D (02-May) YOUR ANSWER

This choice implies a probability of 2 out of 5, which is not applicable, as there are only 6 total combinations. Therefore, this choice misrepresents the actual likelihood of selecting the pair that sums to 21.

E (01-Feb) YOUR ANSWER

This option signifies a probability of 1 out of 2, which is incorrect as well. Given that the number of successful combinations is only 1, this choice fails to accurately depict the situation of selecting two papers.

Conclusion

The only combination of integers from the set {9, 10, 11, 12} that yields a sum of 21 is the pair 10 and 11. Given the total number of possible combinations is 6, the probability of drawing this specific pair is correctly represented as 01-Jun. Thus, understanding the basics of combinations leads to determining the correct likelihood of achieving the desired sum.

The probability that the sum of the integers on the chosen pieces of paper will be 21 is 01-Jun.

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