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Jannie appeared in two exams and the probability of Jannie qualifying

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ktzsikka
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Jannie appeared in two exams and the probability of Jannie qualifying [#permalink] New post   07 Nov 2021, 10:26
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57% (01:37) correct 43% (01:40) wrong based on 93 sessions
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Jannie appeared in two exams and the probability of Jannie qualifying exactly one of the exams is 0.30. what is the probability that Jannie will qualify in both the exams?

1. The probability of Jannie qualifying none of the exam is 0.30

2. The probability of Jannie qualifying either both the exams or none of the exam is 0.70
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ktzsikka
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Re: Jannie appeared in two exams and the probability of Jannie qualifying [#permalink] New post   08 Nov 2021, 11:31
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Here is the OE

Solution:

Step 1: Analyse Question Stem
Jannie appeared in two exams
Probability of Jannie qualifying exactly one of the exams = 0.30
There are 3 possible cases
Jannie will qualify in both the exams
Jannie will qualify in exactly one of the exams
Jannie will qualify in none of the exams
We need to find the probability of Jannie qualifying both the exams.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The probability of Jannie qualifying none of the exam is 0.30

Probability of qualifying both the exam + exactly one of exams + none of exam=1
Probability of qualifying both the exams+ 0.30 + 0.30=1
Probability of qualifying both the exams = 1- 0.60 = 0.40
Hence, statement 1 is sufficient, we can eliminate options B, C, and E.

Statement 2: The probability of Jannie qualifying either both the exams or none of the exam is 0.70

Probability of qualifying both the exams + none of the exam = 0.70
Using just this information we cannot find the probability of qualifying both the exams.

Hence, statement 2 is not sufficient, the correct answer is Option A.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question
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Re: Jannie appeared in two exams and the probability of Jannie qualifying [#permalink] New post   04 Dec 2022, 09:29
Why is the probability of qualifying in only exam two not considered?
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Re: Jannie appeared in two exams and the probability of Jannie qualifying [#permalink] New post   04 Dec 2022, 11:28
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Expert Reply
ktzsikka wrote:
Jannie appeared in two exams and the probability of Jannie qualifying exactly one of the exams is 0.30. what is the probability that Jannie will qualify in both the exams?

1. The probability of Jannie qualifying none of the exam is 0.30

2. The probability of Jannie qualifying either both the exams or none of the exam is 0.70


Solution:
Pre Analysis:
  • Let the two exams be A and B
  • We are given that probability of Jannie qualifying exactly one of the exams is 0.30
  • This means \(P(A).P(B')+P(A').P(B)=0.3......(i)\)
  • We know \(P(A).P(B)+P(A).P(B')+P(A').P(B)+P(A').P(B')=1......(ii)\)
  • We are asked the probability that Jannie will qualify in both exams i.e., the value of \(P(A).P(B)\)

Statement 1: The probability of Jannie qualifying none of the exam is 0.30
  • According to this statement, \(P(A').P(B')=0.3\)
  • We already know \(P(A).P(B')+P(A').P(B)=0.3......(i)\)
  • We can plug both the above values in \(eq (ii)\) to get the answer i.e., the value of \(P(A).P(B)\)
  • Thus, statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2: The probability of Jannie qualifying either both the exams or none of the exam is 0.70
  • According to this statement, \(P(A).P(B)+P(A').P(B')=0.7\)
  • This is sort of redundant information because we knew it from question stem itself when we derived equations i and ii

Hence the right answer is Option A
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Re: Jannie appeared in two exams and the probability of Jannie qualifying [#permalink]
04 Dec 2022, 11:28
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