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D
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Difficulty:
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63% (02:10) correct
37%
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wrong
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Each of the four children has a bag with five different colored discs in it; red blue green yellow and orange. If each child in succession randomly chooses exactly one disc from his bag to flip into a hat. What is the probability that hat will no hold no repeated colours at the end flipping?
A- 1/5
B- 6/625
C- 24/625
D- 24/125
E- 6/125
A- 1/5
B- 6/625
C- 24/625
D- 24/125
E- 6/125
Either OA given by 800score is wrong or my understanding is wrong. Cos my answer is D.
EDIT---OA edited as per Gmat Insight Answer.
EDIT---OA edited as per Gmat Insight Answer.
Updated on: 19 Sep 2021, 13:15
Originally posted by BrentGMATPrepNow on 26 Jun 2017, 13:53.
Last edited by BrentGMATPrepNow on 19 Sep 2021, 13:15, edited 2 times in total.
Last edited by BrentGMATPrepNow on 19 Sep 2021, 13:15, edited 2 times in total.
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sahil7389
As with most probability questions on the GMAT, we can use either counting techniques or probability rules.
Let's use probability rules:
P(no repeated colors) = P(ANY color disc is chosen 1st AND color of 2nd disc is different from 1st disc AND color of 3rd disc is different from 1st and 2nd disc AND color of 4th disc is different from other discs)
= P(ANY color disc is chosen 1st) x P(color of 2nd disc is different from 1st disc) x P(color of 3rd disc is different from 1st and 2nd disc) x P(color of 4th disc is different from other discs)
= 1 x 4/5 x 3/5 x 2/5
= 24/125
Answer: D
08 Aug 2015, 07:01
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sahil7389
ALTERNATE:
The first child can choose any disc out of 5 so probability of him choosing a disc of different color = 5/5 = 1
The Second child can choose any disc out of remaining 4 Colours so probability of him choosing a disc of different colour = 4/5
The Third child can choose any disc out of remaining 3 Colours so probability of him choosing a disc of different colour = 3/5
The Forth child can choose any disc out of remaining 2 Colours so probability of him choosing a disc of different colour = 2/5
Finanl Probability of all the events to happen simultaneously = (5/5)*(4/5)*(3/5)*(2/5) = 24/125
Answer: option D
