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09 Nov 2023, 02:31
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
65% (01:53) correct
35%
(01:54)
wrong
based on 199
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A jar contains marbles of several different colors. Some marbles are to be taken from the jar one at a time, examined and the put back in the jar. What is the probability that exactly three of next five marbles taken from the jar will be blue?
(1) The probability that all of the next five marbles taken from the jar are blue is 243/3125 .
(2) The probability that none of the next five marbles taken from the jar are blue is 32/3125.
(1) The probability that all of the next five marbles taken from the jar are blue is 243/3125 .
(2) The probability that none of the next five marbles taken from the jar are blue is 32/3125.
11 Nov 2023, 01:55
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Bunuel
If we can find the # of Blue marbles and the total # of all marbles we can solve this question.
(1) The probability that all of the next five marbles taken from the jar are blue is 243/3125 .
Let B be the # of Blue marbles and T be the total of all marbles
Prob. of one Blue = B/T
Prob. of two Blue = B/T*B/T
...
Prob. of five Blue = (B/T)^5 = \(\frac{243}{3125}\) -> B/T = 3/5
Since now we know we have \(3\) blue and \(2\) Non Blue marbles. This is suff.
SUFF.
(2) The probability that none of the next five marbles taken from the jar are blue is 32/3125.
Prob. of one Non Blue = NB/T
Prob. of two Non Blue = NB/T*NB/T
...
Prob. of five Non Blue = (NB/T)^5
(NB/T )^5 = \(\frac{32}{3125}\)
NB/T = 2/5
NB = 2
Total = 5
Blue = 3
Similar to statement (1) now we know we have \(3\) blue and \(2\) Non Blue marbles.
SUFF.
Ans D
Hope it helped.
20 Nov 2024, 03:33
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