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In a bag, there are 10 red, 15 green, and 12 blue marbles...
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06 Oct 2020, 03:41
06 Oct 2020, 03:41
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Question Stats:
41% (01:46) correct
58% (01:50) wrong based on 29 sessions
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In a bag, there are 10 red, 15 green, and 12 blue marbles. If you draw two marbles (without replacing), what is the approximate probability of drawing two different colors?
A. None of the other answers
B. 33.33%
C. 25%
D. 67.57%
E. 0.06%
A. None of the other answers
B. 33.33%
C. 25%
D. 67.57%
E. 0.06%
Re: In a bag, there are 10 red, 15 green, and 12 blue marbles...
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06 Oct 2020, 03:53
06 Oct 2020, 03:53
2
The probability of drawing 2 different colors is the same as 1 minus the probability of drawing only the same color. The probability of drawing the same color is:
P(consecutive blue) OR P(consecutive green) OR P(consecutive red) = (10/37)(9/36) + (15/37)(14/36) + (12/37)(11/36) = 432/1332
1 - (432/1332) = 900/1332 ~= 0.6757 = 67.57%
P(consecutive blue) OR P(consecutive green) OR P(consecutive red) = (10/37)(9/36) + (15/37)(14/36) + (12/37)(11/36) = 432/1332
1 - (432/1332) = 900/1332 ~= 0.6757 = 67.57%
In a bag, there are 10 red, 15 green, and 12 blue marbles...
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30 Aug 2022, 07:40
30 Aug 2022, 07:40
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Solution -
Calculate the chance of drawing either two reds, two greens, or two blues. Then, subtract this from 1 (100%) to calculate the possibility of drawing a pair of different colours.
The combined probability of RR, GG, and BB is: (10 * 9) / (37 * 36) + (15 * 14) / (37 * 36) + (12 * 11) / (37 * 36)
This simplifies to: (90 + 210 + 132) / 1332 = 432 / 1332
Subtract from 1: 1 - 432 / 1332 = (1332 - 432) / 1332 = approx. 0.6757 or 67.57%
Answer Choice D
Calculate the chance of drawing either two reds, two greens, or two blues. Then, subtract this from 1 (100%) to calculate the possibility of drawing a pair of different colours.
The combined probability of RR, GG, and BB is: (10 * 9) / (37 * 36) + (15 * 14) / (37 * 36) + (12 * 11) / (37 * 36)
This simplifies to: (90 + 210 + 132) / 1332 = 432 / 1332
Subtract from 1: 1 - 432 / 1332 = (1332 - 432) / 1332 = approx. 0.6757 or 67.57%
Answer Choice D
