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?
In a bulb factory there are different kinds of bulbs, what i
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(1) There are three times as many halogens than any other bulb in the factory.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?
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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