Question 231070: In a piggy bank, there are twice as many dimes as quarters, five times as many nickels as quarters, and twice as many pennies as all other coins combined. It is equally likely that any one of the coins will fall out when the piggy bank is turned upside down. Calculate the probability that either a nickel or a quarter will fall out. Express your solution as a fraction in lowest terms.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a piggy bank, there are twice as many dimes as quarters,
d = 2q
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five times as many nickels as quarters,
n = 5q
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and twice as many pennies as all other coins combined.
p = 2(n + d + q)
(1/2)p - n - d - q = 0
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Rearrange:
0p + 0n + d -2q = 0
0p + n +0d -5q = 0
(1/2)p-n- d - q = 0
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Change to an augmented matrix:
0p + 0n + d = 2q
0p + n +0d = 5q
p - 2n -2d = 2q
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Solve p,d,and n for q:
d = 2q from the 1st equation:
n = 5q
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p = 2(5q)+2(2q)+ 2q
p = 16q
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There are a total of 24q coins
P(q) = 1/24 ; P(p)=16/24; P(n)=5/24 ; P(d)= 2/24
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Calculate the probability that either a nickel or a quarter will fall out. Express your solution as a fraction in lowest terms.
P(nickel or quarter) = P(nickel) + P(quarter) = (5/24)+(1/24) = 1/4
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Cheers,
Stan H.
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