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A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn

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Bunuel
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A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn [#permalink] New post  13 Nov 2018, 02:02
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A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn randomly from the jar, what is the probability that they will be different colors?


A. 3/25

B. 6/25

C. 2/5

D. 3/10

E. 3/5
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Re: A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn [#permalink] New post  13 Nov 2018, 02:09
3c1*2c1/5c2 = 3/5. Answer E

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Re: A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn [#permalink] New post  13 Nov 2018, 02:24
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Bunuel wrote:
A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn randomly from the jar, what is the probability that they will be different colors?


A. 3/25

B. 6/25

C. 2/5

D. 3/10

E. 3/5


Probability that both are red = 3/5 * 2/4 = 6/20 = 3/10

Probability that both are blue = 2/5 * 1/4 = 2/20 = 1/10

The probability that the marbles are different = 1 - probability the marbles are not different = 1 - (3/10 + 1/10) = 1 - (4/10) = 6/10 = 3/5

Alternatively, the probability they are different = 3/5 * 2/4 = 3/10 here we choose the red first then blue

2/5 * 3/4 = 6/20 = 3/10 here we choose the blue first then the red.

3/10 + 3/10 = 6/10 = 3/5 Answer choice E
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Re: A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn [#permalink] New post  13 Nov 2018, 04:36
Bunuel wrote:
A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn randomly from the jar, what is the probability that they will be different colors?


A. 3/25

B. 6/25

C. 2/5

D. 3/10

E. 3/5


P red * P blue= (3/5)*(2/4)= 6/20=3/10
P blue * P red= (2/5)* (3/4)= 3/10

3/10+3/10= 6/10=3/5 E
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Re: A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn [#permalink] New post  14 Nov 2018, 07:33
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Prob of getting 1 red marble is 3C1 = 3
Prob of getting 1 blue marble is 2C1 = 2
Prob of getting 2 marbles is 5C2 = 10
Now 3*2/10
= 3/5
E is the answer

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MathRevolution
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Re: A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn [#permalink] New post  10 Jan 2021, 01:06
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Total marbles: 5

Red: 3
Blue: 2

Two marbles are drawn randomly from the jar: ^5{C_2} = 10

The probability that they will be different colors: '1' from each = ^3{C_1} * ^2{C_1} = 3 * 2 = 6

Probability: \(\frac{6}{10} = \frac{3}{5}\)

Answer E
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Re: A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn [#permalink] New post  25 Aug 2022, 07:55
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A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn randomly from the jar, what is the probability that they will be different colors?


A. 3/25

B. 6/25

C. 2/5

D. 3/10

E. 3/5
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Re: A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn [#permalink] New post  26 Nov 2023, 22:02
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Re: A jar contains 5 marbles: 3 red and 2 blue. If two marbles are drawn [#permalink]
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