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17 Mar 2021, 03:00
Kudos
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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:
85%
(hard)
Question Stats:
46% (02:17) correct
54%
(02:42)
wrong
based on 137
sessions
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Not Attempted Yet
If \(\frac{1 - P}{3}\), \(\frac{4P - 1}{2}\), and \(\frac{6P - 1}{4}\) are the probabilities of three mutually exclusive events, then P lies in which of the following intervals?
A. \(\frac{1}{14} < P < \frac{1}{7}\)
B. \(\frac{5}{38} < P < \frac{17}{38}\)
C. \(\frac{1}{6} < P < \frac{7}{38}\)
D. \(\frac{5}{38} < P < 1\)
E. \(\frac{17}{38} < P < \frac{21}{38}\)
A. \(\frac{1}{14} < P < \frac{1}{7}\)
B. \(\frac{5}{38} < P < \frac{17}{38}\)
C. \(\frac{1}{6} < P < \frac{7}{38}\)
D. \(\frac{5}{38} < P < 1\)
E. \(\frac{17}{38} < P < \frac{21}{38}\)
17 Mar 2021, 07:47
Kudos
Bookmarks
Bunuel
We know nothing about other possible probabilities, not mentioned in question, in which P is used.
Thus, two cases are possible:
A. \(\frac{1 - P}{3} + \frac{4P - 1}{2} + \frac{6P - 1}{4} > 0\)
B. \(\frac{1 - P}{3} + \frac{4P - 1}{2} + \frac{6P - 1}{4} < 1\)
A gives \(P > \frac{5}{38}\)
B gives \(P < \frac{17}{38}\)
Hence, \(\frac{5}{38} < P < \frac{17}{38}\) i.e. 0.13 < P < 0.44
A and E are gone easily. D is not always true.
However, B is 0.25 < P < 0.44 and C is 0.16 < P < 0.18. Both satisfy the condition.
Answer is one of B or C.
Bunuel Please check the options.
