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28 Oct 2021, 02:45
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87% (02:33) correct
13%
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Maria bought 4 black and a certain number of red and blue pencils at 15 cents each an carried them home in one bag. After Maria came home, she took out one pencil at random to write a note and then put the pencil back into the bag. Some time later, she needed to write another note and again took out a pencil from the bag. If the probability that Maria wrote both her notes in black is 1/36, how much did she spend on all pencils?
A. $3
B. $3.2
C. $3.4
D. $3.6
E. $3.8
A. $3
B. $3.2
C. $3.4
D. $3.6
E. $3.8
28 Oct 2021, 04:40
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Bunuel
Maria bought 4 black and a certain number of red and blue pencils at 15 cents each an carried them home in one bag. After Maria came home, she took out one pencil at random to write a note and then put the pencil back into the bag. Some time later, she needed to write another note and again took out a pencil from the bag. If the probability that Maria wrote both her notes in black is 1/36, how much did she spend on all pencils?
A. $3
B. $3.2
C. $3.4
D. $3.6
E. $3.8
A. $3
B. $3.2
C. $3.4
D. $3.6
E. $3.8
If the total pencils are t, the probability of picking first as black = 4/t.
As it is again replaced, the probability in next will also be the same = 4/t
P to pick black pencil in both picks = \(\frac{4}{t}*\frac{4}{t}=\frac{1}{36}\)
\(t^2=16*36…….t=4*6=24\)
Price of these 24 pencils = 15*24 = $3.6
D
28 Oct 2021, 05:21
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This is a bit like asking "what is the probability it rained yesterday?" She has already written the notes; they were either both written in black or they weren't. Probability doesn't come into it.
If the probability something happens is p, then the probability it happens twice in two tries is p^2. So if p is the probability of picking a black pencil (with replacement), we learn that p^2 = 1/36, so p = 1/6, and one sixth of the pencils are black. We have 4 black pencils, so 24 pencils in total, which cost $0.15*24 = $3.60.
If the probability something happens is p, then the probability it happens twice in two tries is p^2. So if p is the probability of picking a black pencil (with replacement), we learn that p^2 = 1/36, so p = 1/6, and one sixth of the pencils are black. We have 4 black pencils, so 24 pencils in total, which cost $0.15*24 = $3.60.
