Bunuel wrote:
Bert has $1.37 of loose change in his pocket — pennies ($0.01), nickels ($0.05), dimes ($0.10), and quarters ($0.25). He reaches into his pocket and pulls out one coin at random. What is the probability that the coin is a nickel?
(1) There are exactly seven pennies in his pocket
(2) There are exactly three quarters in his pocket
MAGOOSH OFFICIAL SOLUTION:A reminder for non-American students — $1.00 = 100¢. Thus
penny = $0.01 = 1¢
nickel = $0.05 = 5¢
dime = $0.10 = 10¢
quarter = $0.25 = 25¢
Statement #1: Bert has seven pennies, amounting to 7¢. The other coins total $1.30. This could be all nickels — 26 nickels — so that of the 7 + 26 = 33 coins in the pocket, 26 are nickel, and the probability of picking a nickel would be 26/33. Or, that $1.30 could be 4 quarters and 3 dimes, so that there were no nickels, and the probability of picking a nickel would be zero! Different possible choices lead to different answer to the prompt question, so this statement, alone and by itself, is insufficient.
Statement #2: Bert has three quarters, amounting to 75¢. The other coins total 62¢ — this could be two pennies and twelve nickels, that of the 3 + 2 + 12 = 17 coins in the pocket, 12 are nickels, and the probability is 12/17. Or, that 62¢ could be entirely in pennies, without any nickels or dimes at all: then the probability of picking a nickel would be zero. Different possible choices lead to different answer to the prompt question, so this statement, alone and by itself, is insufficient.
Combined statements: Now, we know Bert has seven pennies and three quarters, and these ten coins together account for 82¢. The remaining 55¢ must be composed of dimes and nickels. There could be eleven nickels and no dimes, so that of the 10 + 11 = 21 coins in the pocket, 11 are nickels, and P = 11/21. OR, there could be five dimes and one nickel in the pocket, so of the 10 + 5 + 1 = 16 coins in the pocket, only one is a nickel, and P = 1/16. Different possible choices lead to different answer to the prompt question, so both statements combined are insufficient.
Nothing is sufficient.
Answer = E
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03 Mar 2021, 14:08
82%
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