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24 Mar 2021, 08:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
81% (01:42) correct
19%
(01:42)
wrong
based on 131
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A certain jar contains 5 marbles, r of which are red. If two marbles are to be selected at random, and the probability that both marbles will be red is \(\frac{1}{10}\), what is the value of r?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
rvgmat12
Joined: 19 Oct 2014
Last visit: 27 Mar 2026
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24 Mar 2021, 13:58
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(r/5)*(r-1)/4 = 1/10
r.(r-1) = 2
r = 2
B.
Posted from my mobile device
r.(r-1) = 2
r = 2
B.
Posted from my mobile device
31 Mar 2021, 09:12
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Bunuel
Solution:
The probability that the first marble selected is red is r/5, and the probability that the second marble selected is red is (r - 1)/4. Therefore, we can create the equation:
r/5 x (r - 1)/4 = 1/10
r(r - 1)/20 = 2/20
r(r - 1) = 2
r^2 - r - 2 = 0
(r - 2)(r + 1) = 0
r = 2 or r = -1
Since r can’t be negative, r = 2.
Alternate Solution:
If there is only one red marble, the probability of selecting two red marbles is zero. If there are five red marbles, the probability of selecting two red marbles is one. Therefore, we eliminate answer choices A and E. Let’s test the remaining answer choices.
If there are two red marbles, then the probability of selecting two red marbles is 2/5 x 1/4 = 2/20 = 1/10. Thus, there are two red marbles in the jar.
Answer: B
