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Out of a box that contains 4 black and 6 white mice, three are randoml
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22 Oct 2021, 06:58
22 Oct 2021, 06:58
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Out of a box that contains 4 black and 6 white mice, three are randomly chosen. What is the probability that all three will be black?
a) 8/125.
b) 1/30.
c) 2/5.
d) 1/720.
e) 3/10.
a) 8/125.
b) 1/30.
c) 2/5.
d) 1/720.
e) 3/10.
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Re: Out of a box that contains 4 black and 6 white mice, three are randoml
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22 Oct 2021, 07:20
22 Oct 2021, 07:20
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Carcass wrote:
Out of a box that contains 4 black and 6 white mice, three are randomly chosen. What is the probability that all three will be black?
a) 8/125.
b) 1/30.
c) 2/5.
d) 1/720.
e) 3/10.
a) 8/125.
b) 1/30.
c) 2/5.
d) 1/720.
e) 3/10.
Solution #1: Probability rules
P(all 3 selected mice are black) = P(1st mouse is black AND 2nd mouse is black AND 3rd mouse is black)
= P(1st mouse is black) x P(2nd mouse is black) x P(3rd mouse is black)
= 4/10 x 3/9 x 2/8
= 1/30
= B
Solution #2: counting methods:
P(all 3 mice are black) = (# of ways to select 3 black mice)/(TOTAL # of ways to select ANY 3 mice)
# of ways to select 3 black mice
Since the order in which we select the mice does not matter, we can use COMBINATIONS
We can select 3 black mice from 4 black mice in 4C3 ways (= 4 ways)
TOTAL # of ways to select ANY 3 mice
We can select 3 mice from all 10 mice in 10C3 ways (= 120 ways)
ASIDE: If anyone is interested, we have a video on calculating combinations in your head (below)
So, P(all 3 mice are black) = 4/120
= 1/30
= B
gmatclubot
Re: Out of a box that contains 4 black and 6 white mice, three are randoml [#permalink]
22 Oct 2021, 07:20
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