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The probability that John will pass in all subjects in final Exam is 0

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The probability that John will pass in all subjects in final Exam is 0 [#permalink] New post   29 Sep 2018, 10:00
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Weekly Quant Quiz Question -1



The probability that John will pass in all subjects in final Exam is 0.69 and the probability that John will be promoted to next class is 0.73. What is the greatest probability that neither of the two events will occur.
a) 0.11
b) 0.27
c) 0.41
d) 0.56
e) 0.62
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Re: The probability that John will pass in all subjects in final Exam is 0 [#permalink] New post   29 Sep 2018, 11:04
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p(pass in all subjects)=0.69 is just a subset of P(promoted to next class)=0.73. What this means is that of all the students that get promoted to next class, few(0.69) will pass in all subjects.

Hence those who neither pass in all subjects not get promoted can not be more than 1-0.73 = 0.27, and hence the answer is B
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Re: The probability that John will pass in all subjects in final Exam is 0 [#permalink] New post   29 Sep 2018, 10:08
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Please find solution attached. IMO B.
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Re: The probability that John will pass in all subjects in final Exam is 0 [#permalink] New post   29 Sep 2018, 10:07
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P(Pass) = 0.69
P(Not Pass ) = 1- 0.69 = 0.31

P(Promoted) = 0.73
P(Not Promoted) = 1-0.73 = 0.27

P(Neither) = 0.31+0.27=0.56
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Re: The probability that John will pass in all subjects in final Exam is 0 [#permalink] New post   29 Sep 2018, 10:25
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Total outcome= A + B+ Both+ none.

We have to maximize the probability and so we have to minimzie other outcomes.
The greatest subset given is .73 which can include .69

hence think of the problem as a big subset which includes a smaller subject. Whatever left is the neither .

SO answer = 1-.73 =.27
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Re: The probability that John will pass in all subjects in final Exam is 0 [#permalink] New post   29 Sep 2018, 15:39
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The probability that John will pass in all subjects in final Exam is 0.69 and the probability that John will be promoted to next class is 0.73. What is the greatest probability that neither of the two events will occur.

Probability that John will not pass in all final subjects= 1- 0.69= .31
Probability that he will not be promoted to next class is 1-0.73 = .27

Greatest probability that neither of these two event occur is .27
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Re: The probability that John will pass in all subjects in final Exam is 0 [#permalink] New post   29 Sep 2018, 10:14
B, 0.27

seek the biggest probability for John to occur in the events, then the rest of it it's the probability for John to not occur in the event. Because the opposite from the biggest probability for the events to occur is the probability for the things will not occur

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Re: The probability that John will pass in all subjects in final Exam is 0 [#permalink] New post   29 Sep 2018, 10:17
Probability is .27

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Re: The probability that John will pass in all subjects in final Exam is 0 [#permalink] New post   29 Sep 2018, 10:30
X(failUnotpromoted)=x(fail)+x(notpromoted)-x(failINTERSECTION notpormoted)
=0.31+0.27-0.31*0.27
=0.53
Asnwer=D
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Re: The probability that John will pass in all subjects in final Exam is 0 [#permalink] New post   28 Mar 2024, 23:38
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Re: The probability that John will pass in all subjects in final Exam is 0 [#permalink]
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