Caselets

Q: What is the value of 'x' (the number of Green balls in Bag C)?

Correct Answer: Option B (8). Total balls in Bag C = 6 + x + 4 = 10 + x. Probability of Red = 6 / (10 + x) = 1/3. 18 = 10 + x => x = 8.

Q: If two balls are drawn at random from Bag A without replacement, what is the probability that both are Green?

Correct Answer: Option A (1/11). Bag A has 5R, 4G, 3B (Total 12). P(both Green) = (4/12) * (3/11) = (1/3) * (3/11) = 1/11.

Q: One ball is drawn from Bag B and one ball is drawn from Bag C. What is the probability that both are Blue?

Correct Answer: Option A (4/45). Bag B has 6 Blue out of 15. Bag C has 4 Blue out of 18 (since x=8). P(Blue from B) = 6/15 = 2/5. P(Blue from C) = 4/18 = 2/9. P(both Blue) = (2/5) * (2/9) = 4/45.

Q: If all balls from Bag A and Bag B are poured into a single large bag, and one ball is drawn, what is the probability that it is a Red ball?

Correct Answer: Option A (1/3). Total Red = 5 (from A) + 4 (from B) = 9. Total balls = 12 (from A) + 15 (from B) = 27. P(Red) = 9 / 27 = 1/3.

Q: Three balls are drawn from Bag C with replacement. What is the probability that exactly one of them is Green?

Correct Answer: Option A (100/243). Bag C: 6R, 8G, 4B (Total 18). P(Green) = 8/18 = 4/9. P(Not Green) = 10/18 = 5/9. We want exactly 1 Green in 3 trials. Number of ways = 3C1 = 3. Probability = 3 * (4/9) * (5/9)^2 = 3 * (4/9) * (25/81) = 300 / 729 = 100 / 243.

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Practice Caselets questions with answers and step-by-step solutions. These problems are curated from recent campus placement test papers (TCS, Infosys, Wipro, Cognizant, Accenture) and competitive government exams (SSC CGL, Bank PO, RRB NTPC, UPSC).

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Caselets: Reference Passage & Data Shared for questions below

Caselet Context & PassageSet 5: Probability

There are three bags: Bag A, Bag B, and Bag C. Bag A contains 5 Red, 4 Green, and 3 Blue balls. Bag B contains 4 Red, 5 Green, and 6 Blue balls. Bag C contains 6 Red, 'x' Green, and 4 Blue balls. The probability of drawing a Red ball at random from Bag C is exactly 1/3.

Q41

What is the value of 'x' (the number of Green balls in Bag C)?

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Q42

If two balls are drawn at random from Bag A without replacement, what is the probability that both are Green?

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Q43

One ball is drawn from Bag B and one ball is drawn from Bag C. What is the probability that both are Blue?

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Q44

If all balls from Bag A and Bag B are poured into a single large bag, and one ball is drawn, what is the probability that it is a Red ball?

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Q45

Three balls are drawn from Bag C with replacement. What is the probability that exactly one of them is Green?

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Caselets

What is the value of 'x' (the number of Green balls in Bag C)?

Community Discussion & Shortcut Formulas

If two balls are drawn at random from Bag A without replacement, what is the probability that both are Green?

Community Discussion & Shortcut Formulas

One ball is drawn from Bag B and one ball is drawn from Bag C. What is the probability that both are Blue?

Community Discussion & Shortcut Formulas

If all balls from Bag A and Bag B are poured into a single large bag, and one ball is drawn, what is the probability that it is a Red ball?

Community Discussion & Shortcut Formulas

Three balls are drawn from Bag C with replacement. What is the probability that exactly one of them is Green?

Community Discussion & Shortcut Formulas