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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
A box contains 2 black balls and 2 white balls. If 2 balls are randoml
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13 Jun 2022, 07:16
13 Jun 2022, 07:16
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Question Stats:
83% (00:55) correct
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A box contains 2 black balls and 2 white balls. If 2 balls are randomly selected from the box, without replacement, what is the probability the two balls are different colors?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A box contains 2 black balls and 2 white balls. If 2 balls are randoml
[#permalink]
15 Jun 2022, 05:47
15 Jun 2022, 05:47
2
GreenlightTestPrep wrote:
A box contains 2 black balls and 2 white balls. If 2 balls are randomly selected from the box, without replacement, what is the probability the two balls are different colors?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
No takers???
Here's my solution...
P(different colors) = P(1st ball is white AND 2nd ball is black OR 1st ball is black AND 2nd ball is white)
= [P(1st ball is white) x P(2nd ball is black)] + [P(1st ball is black) x P(2nd ball is white)]
= [2/4 x 2/3] + [2/4 x 2/3]
= 1/3 + 1/3
= 2/3
Answer: D
Re: A box contains 2 black balls and 2 white balls. If 2 balls are randoml
[#permalink]
15 Jun 2022, 07:56
15 Jun 2022, 07:56
1
I thought of this problem a different way.
The chance that both balls are white:
(2/4)(1/3)=1/6
The chance that both balls are black:
(2/4)(1/3)=1/6
The chance that both are the same color:
(1/6)+(1/6)=2/6
The chance that both are different colors:
1-(2/6)=4/6=2/3
D
The chance that both balls are white:
(2/4)(1/3)=1/6
The chance that both balls are black:
(2/4)(1/3)=1/6
The chance that both are the same color:
(1/6)+(1/6)=2/6
The chance that both are different colors:
1-(2/6)=4/6=2/3
D
