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A bag contains pens of four brands – P, Q, R, and S. Number of brand P pens are L, brand Q pens are M, brand S pens are 8 and brand R pens are (L + 2). Find the probability of picking two pens at randomly such that one is of brand Q and one is of brand S.
Statement I. Probability of picking two pens at randomly such that one is brand P and one is brand R is 12/95.
Statement II. Value of M is 2 less than that of L.
Statement III. Probability of picking two pens of brand P without replacement from bag is 3/95.
  • a)
    Statement I and II together is sufficient to answer the question
  • b)
    Statement II and III together is sufficient to answer the question
  • c)
    Statement III and I together is sufficient to answer the question
  • d)
    Any two statements together are sufficient to answer the question
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A bag contains pens of four brands – P, Q, R, and S. Number of brand ...
Total pens in the bag = L + M + L + 2 + 8 = 2L + M + 10
From (I + II),
M = L – 2
Total balls in the bag = 2L + L – 2 + 10 = 3L + 8
Now,
{2 x L x (L + 2)} / {(3L +8) x (3L + 7)} = 12/95
On solving we get L = 4
So, M = 2
Brand Q pens in the bag = 2
Brand S pens in the bag = 8
Total pens in the bag = 20
Required probability = 2 x 8 x 2 / 20 x 19 = 8/95
This combination is sufficient to answer the question.
On combining II and III,
[L/ (3L + 8)] x [(L – 1)/ (3L + 7)] = 3/95
On solving we get L = 4
M = 2
Total pens in the bag = 20
Required probability = 2 x 8 x 2 / 20 x 19 = 8/95
On combining III and I,
2 x L x (L + 2) / (Total balls) x (total balls – 1) = 12/95
Also,
L x (L – 1) / (Total balls) x (total balls – 1) = 3/95
From both equations, we get
L x (L + 2) = 2 x L x (L – 1)
L + 2 = 2L – 2
So, value of L = 4
So, (2L + M + 10) x (2L + M + 9) = 4 x 95
(18 + M) x (17 + M) = 20 x 19
So, value of M = 2
Total pens in the bag = 20
Required probability = 2 x 8 x 2 / 20 x 19 = 8/95
Hence, answer is option D
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A bag contains pens of four brands – P, Q, R, and S. Number of brand P pens are L, brand Q pens are M, brand S pens are 8 and brand R pens are (L + 2). Find the probability of picking two pens at randomly such that one is of brand Q and one is of brand S.Statement I. Probability of picking two pens at randomly such that one is brand P and one is brand R is 12/95.Statement II. Value of M is 2 less than that of L.Statement III. Probability of picking two pens of brand P without replacement from bag is 3/95.a)Statement I and II together is sufficient to answer the questionb)Statement II and III together is sufficient to answer the questionc)Statement III and I together is sufficient to answer the questiond)Any two statements together are sufficient to answer the questione)None of theseCorrect answer is option 'D'. Can you explain this answer?
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A bag contains pens of four brands – P, Q, R, and S. Number of brand P pens are L, brand Q pens are M, brand S pens are 8 and brand R pens are (L + 2). Find the probability of picking two pens at randomly such that one is of brand Q and one is of brand S.Statement I. Probability of picking two pens at randomly such that one is brand P and one is brand R is 12/95.Statement II. Value of M is 2 less than that of L.Statement III. Probability of picking two pens of brand P without replacement from bag is 3/95.a)Statement I and II together is sufficient to answer the questionb)Statement II and III together is sufficient to answer the questionc)Statement III and I together is sufficient to answer the questiond)Any two statements together are sufficient to answer the questione)None of theseCorrect answer is option 'D'. Can you explain this answer? for Banking Exams 2024 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about A bag contains pens of four brands – P, Q, R, and S. Number of brand P pens are L, brand Q pens are M, brand S pens are 8 and brand R pens are (L + 2). Find the probability of picking two pens at randomly such that one is of brand Q and one is of brand S.Statement I. Probability of picking two pens at randomly such that one is brand P and one is brand R is 12/95.Statement II. Value of M is 2 less than that of L.Statement III. Probability of picking two pens of brand P without replacement from bag is 3/95.a)Statement I and II together is sufficient to answer the questionb)Statement II and III together is sufficient to answer the questionc)Statement III and I together is sufficient to answer the questiond)Any two statements together are sufficient to answer the questione)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Banking Exams 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains pens of four brands – P, Q, R, and S. Number of brand P pens are L, brand Q pens are M, brand S pens are 8 and brand R pens are (L + 2). Find the probability of picking two pens at randomly such that one is of brand Q and one is of brand S.Statement I. Probability of picking two pens at randomly such that one is brand P and one is brand R is 12/95.Statement II. Value of M is 2 less than that of L.Statement III. Probability of picking two pens of brand P without replacement from bag is 3/95.a)Statement I and II together is sufficient to answer the questionb)Statement II and III together is sufficient to answer the questionc)Statement III and I together is sufficient to answer the questiond)Any two statements together are sufficient to answer the questione)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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