A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
A. 1/2
B. 8/15
C. 7/12
D. 2/3
E. 7/10
Answer: B
Source: Magoosh
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A box contains 4 red chips and 2 blue chips. If two chips are
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BTGModeratorVI
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P(different colors) = P(1st chip is red and 2nd chip is blue OR 1st chip is blue and 2nd chip is red)BTGModeratorVI wrote: ↑Fri May 29, 2020 6:40 amA box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
A. 1/2
B. 8/15
C. 7/12
D. 2/3
E. 7/10
Answer: B
Source: Magoosh
= P(1st chip is red and 2nd chip is blue) + P(1st chip is blue and 2nd chip is red)
= P(1st chip is red) x P(2nd chip is blue) + P(1st chip is blue) x P(2nd chip is red)
= 4/6 x 2/5 + 2/6 x 4/5
= 8/30 + 8/30
= 16/30
= 8/15
Answer: B
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quichopipe
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Probability is (total of favorable outcomes)/(total number of possible outcomes).
Let's let R = a red chip and B = a blue chip. Since we need one chip from each color, we can either pick a red then a blue, or a blue then a red.
RB or BR
There are 4 possible Rs and 2 possible Bs
Case 1: (4C1)*(2C1)
Case 2: (2C1)*(4C1)
This is really just saying (4C1)*(2C1) * 2 which is 16
Now let's look at our denominator
There are 6 chips total (4+2 = 6)
We first want one chip from 6 and then one chip from 5 (no replacement)
(6C1)*(5C1) = 30
So 16/30 = 8/15
Answer choice B.
Let's let R = a red chip and B = a blue chip. Since we need one chip from each color, we can either pick a red then a blue, or a blue then a red.
RB or BR
There are 4 possible Rs and 2 possible Bs
Case 1: (4C1)*(2C1)
Case 2: (2C1)*(4C1)
This is really just saying (4C1)*(2C1) * 2 which is 16
Now let's look at our denominator
There are 6 chips total (4+2 = 6)
We first want one chip from 6 and then one chip from 5 (no replacement)
(6C1)*(5C1) = 30
So 16/30 = 8/15
Answer choice B.
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Solution:BTGModeratorVI wrote: ↑Fri May 29, 2020 6:40 amA box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
A. 1/2
B. 8/15
C. 7/12
D. 2/3
E. 7/10
Answer: B
To satisfy the requirement, we must obtain either R-B or B-R. Thus, we need to determine:
P(red) x P(blue) + P(blue) x R(red)
4/6 x 2/5 + 2/6 x 4/5 = 2/3 x 2/5 + 1/3 x 4/5 = 4/15 + 4/15 = 8/15.
Answer: B
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