1989 AMC 12 Problem 30
Attempt Problem 30 of the 1989 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1989 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
30.
Suppose that boys and girls line up in a row. Let be the number of places in the row where a boy and a girl are standing next to each other. For example, for the row we have The average value of (if all possible orders of these people are considered) is closest to
Answer: A
Small Hint:
Use an indicator for each of the adjacent pairs
Big Hint:
For a fixed adjacent pair, compute the probability of seeing or
Solution:
For each of the adjacent position pairs, the probability of mixed sexes is By linearity of expectation, which is closest to
Thus the correct answer is A.
Problem 30 in Other Years
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