Maria bought 4 black and a certain number of red and blue pencils at 15 cents each an carried them home in one bag. Afte

[Vincen]

Maria bought 4 black and a certain number of red and blue pencils at 15 cents each and 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. Sometime 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

Answer: D

Source: Manhattan GMAT

[swerve]

Maria bought 4 black and a certain number of red and blue pencils at 15 cents each and 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. Sometime 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

Answer: D

Source: Manhattan GMAT

If the total pencils are t, the probability of picking first as black \(= \dfrac{4}{t}.\)

As it is again replaced, the probability in next will also be the same \(= \dfrac{4}{t}.\)

\(P\) to pick black pencil in both picks \(=\dfrac{4}{t} \ast \dfrac{4}{t} = \dfrac{1}{36}\)

\(t^2=16\ast 36 \Longrightarrow t = 4 \ast 6 = 24\)

Price of these \(24\) pencils \(= 15\ast 24 = \$3.6\)

Regards!