Problem 14 · 1990 AJHSME
Medium
Fractions, Decimals & Percents
probabilityfraction-to-count
A bag contains only blue balls and green balls. There are 6 blue balls. If the probability of drawing a blue ball at random from this bag is 14, then the number of green balls in the bag is
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Answer: B — 18.
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Hint 1 of 2
'Probability of blue is 1/4' is just another way of saying 1 out of every 4 balls is blue. If the 6 blue balls *are* that one-quarter, how big is the whole bag?
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Hint 2 of 2
The trap: the answer is the GREEN count, not the total. Find the total first, then take blue away. (1/4 blue means 3/4 green — a nice shortcut.)
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Approach: fraction-to-count, then mind the question (green, not total)
- Probability 1/4 blue means blue is exactly one-quarter of the bag. The 6 blue balls are that quarter, so the full bag is 4 quarters = 4×6 = 24 balls.
- But the question asks for *green*, not the total. Green = 24 − 6 = 18.
- *Shortcut:* if blue is 1/4 of the bag, green is the other 3/4 = 3×6 = 18 directly — the unit '6 = one quarter' lets you scale up any piece.
- *Don't fall for* picking 24 (choice C) — that's the total, the most common slip here.
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