## Monday, July 19, 2010

### Apple a Day Keeps the Barrels Away

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A barrel contains only apples and oranges. There are twice as many apples as oranges. The apples are either red or yellow and 4 times as many red as are yellow. If one piece of fruit is to be drawn at random from the barrel, what is the probability that the piece drawn will be a yellow apple?

1. Hi, this is about working out the number of fruit in the barrel. There must be at least five apples or a factor of five for the ratio to be 4:1 red to yellow, and as there are twice as many apples as oranges, there must be an even number of apples. So the fewest possible apples is 10 (8 red, 2 yellow) along with 5 oranges.
So, the probability of randomly drawing a yellow apple is 2/15 or about 0.1333

2. I used equations to figure it out.
A = # of apples
O = # of oranges
R = # of Red apples
Y = # of Yellow apples
T = # of apples and oranges
Y/T = probability of picking a yellow apple

From the start we know that there are apples and oranges in the barrel, so: A + O = T

We also know that A = 2O

So A + 1/2 A = T => A = 2/3 T (1)

From the second half, we know that R + Y = A and R = 4Y. So, 4Y + Y = A => 5Y = A.

Replace A in (1) and you get 5Y = 2/3 T.

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