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04 Apr 2023, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (01:58) correct
42%
(02:18)
wrong
based on 131
sessions
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A bag contains blue and red balls only.
If one ball is drawn, the probability of selecting a blue ball is 1/2.
If two balls are drawn randomly without replacement, the probability of selecting a blue and then a red ball is 5/18.
Two balls are drawn randomly without replacement, what is the probability of drawing a red ball, given that the first ball drawn was blue?
(A) 2/9
(B) 5/18
(C) 4/9
(D) 1/2
(E) 5/9
If one ball is drawn, the probability of selecting a blue ball is 1/2.
If two balls are drawn randomly without replacement, the probability of selecting a blue and then a red ball is 5/18.
Two balls are drawn randomly without replacement, what is the probability of drawing a red ball, given that the first ball drawn was blue?
(A) 2/9
(B) 5/18
(C) 4/9
(D) 1/2
(E) 5/9
04 Apr 2023, 05:44
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Bunuel
Number of blue balls = b
Number of red balls = r
If one ball is drawn, the probability of selecting a blue ball is 1/2.
\(\frac{b}{b+r} = \frac{1}{2}\)
Upon solving we get
\(b = r\) ---------- (1)
If two balls are drawn randomly without replacement, the probability of selecting a blue and then a red ball is 5/18.
\(\frac{b}{b+r} * \frac{r}{b+r-1} = \frac{5}{18}\)
As b = r, let's replace the same
\(\frac{b}{2b} * \frac{b}{2b-1} = \frac{5}{18}\)
\(\frac{1}{2} * \frac{b}{2b-1} = \frac{5}{18}\)
18b = 20b - 10
b = 5
b = r = 5
Two balls are drawn randomly without replacement, what is the probability of drawing a red ball, given that the first ball drawn was blue?
Number of red balls = 5
Total number of balls remaining = 9
Required probability = 5/9
Option E
11 Apr 2023, 01:48
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Prob. of getting a Blue ball = 1/2
Let the probability of getting a red ball on 2nd draw = A
Prob. of getting a blue ball and then a red ball = 1/2 * A = 5/18. Therefore, A = 5/9
Question is asking about value of A. Hence answer is 5/9.
Let the probability of getting a red ball on 2nd draw = A
Prob. of getting a blue ball and then a red ball = 1/2 * A = 5/18. Therefore, A = 5/9
Question is asking about value of A. Hence answer is 5/9.
