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In a jar there are exactly 56 marbles, each of which is yellow, purple

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Bunuel
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In a jar there are exactly 56 marbles, each of which is yellow, purple [#permalink] New post   27 Oct 2020, 06:00
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In a jar there are exactly 56 marbles, each of which is yellow, purple, or blue. The probability of randomly selecting a yellow marble from the jar is \(\frac{2}{7}\), and the probability of randomly selecting a purple marble from the jar is \(\frac{3}{7}\). How many marbles in the jar are blue?


A. 8
B. 10
C. 12
D. 14
E. 16
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E
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Re: In a jar there are exactly 56 marbles, each of which is yellow, purple [#permalink] New post   27 Oct 2020, 07:29
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Bunuel wrote:
In a jar there are exactly 56 marbles, each of which is yellow, purple, or blue. The probability of randomly selecting a yellow marble from the jar is \(\frac{2}{7}\), and the probability of randomly selecting a purple marble from the jar is \(\frac{3}{7}\). How many marbles in the jar are blue?


A. 8
B. 10
C. 12
D. 14
E. 16




Sum of probabilities of picking a Yellow or Purple or a blue marble = 1

P(Y) + P(P) + P(B) = 1

\(\frac{2}{7} + \frac{3}{7} + P(B) = 1\)

P(B) = \(1 - \frac{3}{7} - \frac{2}{7} = \frac{2}{7}\)


\(Probability = \frac{Favorable \space Outcomes}{Total \space Outcomes}\)

P(B) = \(\frac{2}{7} = \frac{B}{56}\)

B = 16


Option E

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Re: In a jar there are exactly 56 marbles, each of which is yellow, purple [#permalink] New post   27 Oct 2020, 11:36
Bunuel wrote:
In a jar there are exactly 56 marbles, each of which is yellow, purple, or blue. The probability of randomly selecting a yellow marble from the jar is \(\frac{2}{7}\), and the probability of randomly selecting a purple marble from the jar is \(\frac{3}{7}\). How many marbles in the jar are blue?


A. 8
B. 10
C. 12
D. 14
E. 16


total marbles 56
yellow 2/7 *56 ; 16
purple 3/7*56 ; 24
56-40 ; 16 blue color marbles
option E
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Re: In a jar there are exactly 56 marbles, each of which is yellow, purple [#permalink] New post   31 Oct 2020, 13:51
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Bunuel wrote:
In a jar there are exactly 56 marbles, each of which is yellow, purple, or blue. The probability of randomly selecting a yellow marble from the jar is \(\frac{2}{7}\), and the probability of randomly selecting a purple marble from the jar is \(\frac{3}{7}\). How many marbles in the jar are blue?


A. 8
B. 10
C. 12
D. 14
E. 16


Solution:

Since the probability of randomly selecting a yellow marble is 2/7 and that of a purple marble is 3/7, the probability of randomly selecting a blue marble is 1 - 2/7 - 3/7 = 2/7. Since there are 56 marbles in the jar, there are 2/7 x 56 = 2 x 8 = 16 blue marbles in the jar.

Answer: E
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Re: In a jar there are exactly 56 marbles, each of which is yellow, purple [#permalink]
31 Oct 2020, 13:51
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