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06 May 2012, 10:29
Kudos
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A
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Difficulty:
65%
(hard)
Question Stats:
62% (02:30) correct
38%
(02:46)
wrong
based on 396
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For each player's turn in a certain board game, a card is drawn. 3/4 of the cards in the deck are marked with a circle, and the 1/4 remaining cards are marked with a square. If five players draw a card and then return it to the deck, what is the probability that at least four of the cards drawn are marked with a square?
A. (1/4)^3
B. 5(1/4)^3
C. 3/4(1/4)^4
D. 2/3(1/4)^4
E. (1/4)^5
A. (1/4)^3
B. 5(1/4)^3
C. 3/4(1/4)^4
D. 2/3(1/4)^4
E. (1/4)^5
06 May 2012, 10:41
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Galiya
At least four of the cards drawn are marked with a square means 4 or all 5 cards are marked with a square.
\(P=P(SSSSC)+P(SSSSS)=\frac{5!}{4!}*(\frac{1}{4})^4*\frac{3}{4}+(\frac{1}{4})^5=\frac{1}{4^3}\), we are multiplying first case by \(\frac{5!}{4!}\), since SSSSC can occur in several ways: SSSSC, SSSCS, SSCSS, ... Notice that the number of occurrences of SSSSC basically is the number of arrangements of 5 letters SSSSC out of which 4 S's are identical, so it's \(\frac{5!}{4!}\).
Answer: A.
Hope it's clear.
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