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16 Apr 2020, 10:12
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Difficulty:
85%
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Question Stats:
48% (02:10) correct
52%
(02:21)
wrong
based on 110
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A box contains 5 green, 4 yellow and 3 white marbles. Three marbles are drawn at random. What is the probability that they are not of the same color?
A) 3/44
B) 3/55
C) 52/55
D) 41/44
E) 1/22
A) 3/44
B) 3/55
C) 52/55
D) 41/44
E) 1/22
16 Apr 2020, 10:21
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ARIEN3228
A box contains 5 green, 4 yellow and 3 white marbles. Three marbles are drawn at random. What is the probability that they are not of the same color?
A) 3/44
B) 3/55
C) 52/55
D) 41/44
E) 1/22
A) 3/44
B) 3/55
C) 52/55
D) 41/44
E) 1/22
Let's find the probability that three drawn marble are of the same color and subtract that from 1.
P(three marbles are NOT of the same color) = 1 - P(three marbles are of the same color) =
= 1- (P(all three are green) + P(all three are yellow) + P(all three are white)) =
\(= 1- (\frac{5C3}{12C3} + \frac{4C3}{12C3} + \frac{3C3}{12C3}) = \)
\(= 1- (\frac{10}{220} + \frac{4}{220} + \frac{1}{220}) = \frac{41}{44}\).
Answer: D.
17 Apr 2020, 08:22
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Detailed Solution
Let balls are GGGGG, YYYY and WWW.
So, we could solve this question in 2 different ways:
The question can be solved by considering the two scenarios:
1) We can calculate the things that we want in above case scenarios is not the same colour.
2. The things we don't want. In this scenario we can calculate the answer (1 - we don't want ).
So, the scenarios we don't want are:
Probability of Getting a Green ball from the box = (5/12) * (4/11) * (3/10) = 60/1320
Probability of Getting Yellow ball = (4/12) * (3/11) * (2/10) = 24/1320
Probability of Getting White Ball = (3/12) * (2/11) * (1/10) = 6 /1320
So, Probability of getting Green or Yellow or White ball = (60/1320) + (24/1320) + (6/1320) = 9/132 = 3/44.
(1 - we don't want )
1- 3/44
Ans: 41/44.
Let balls are GGGGG, YYYY and WWW.
So, we could solve this question in 2 different ways:
The question can be solved by considering the two scenarios:
1) We can calculate the things that we want in above case scenarios is not the same colour.
2. The things we don't want. In this scenario we can calculate the answer (1 - we don't want ).
So, the scenarios we don't want are:
Probability of Getting a Green ball from the box = (5/12) * (4/11) * (3/10) = 60/1320
Probability of Getting Yellow ball = (4/12) * (3/11) * (2/10) = 24/1320
Probability of Getting White Ball = (3/12) * (2/11) * (1/10) = 6 /1320
So, Probability of getting Green or Yellow or White ball = (60/1320) + (24/1320) + (6/1320) = 9/132 = 3/44.
(1 - we don't want )
1- 3/44
Ans: 41/44.
