ardz24 wrote:In a bulb factory there are different kinds of bulbs, what is the probability that a bulb chosen randomly is a halogen?
(1) There are three times as many halogens than any other bulb in the factory.
(2) The ratio between the halogen to all the other bulbs is 2 to 7.
What's the best way to determine which statement is sufficient?
(1) There are three times as many halogens than any other bulb in the factory.
We do not know how many kinds of bulbs are there.
Case 1: Say there are only two kinds of bulbs -- halogen and tungsten; say the number of tungsten bulbs = 1, then the number of halogen bulbs = 3.
The probability that a bulb chosen randomly is a halogen = 3/(3 + 1) = 3/4.
Case 2: Say there are only three kinds of bulbs -- halogen, mercury, and tungsten; say the number of tungsten bulbs = the number of mercury bulbs = 1, then the number of halogen bulbs = 3.
The probability that a bulb chosen randomly is a halogen = 3/(3 + 1 + 1) = 3/5. No unique answer. Insufficient.
(2) The ratio between the halogen to all the other bulbs is 2 to 7.
Say the number of all the other bulbs = 7, then the number of halogen bulbs = 2.
The probability that a bulb chosen randomly is a halogen = 2/(7 + 2) = 2/9. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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