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Urn 1 has five white and seven black balls. Urn 2 has three white and twelve black balls. We flip a fair coin. If the outcome is head, then a ball from urn 1 is selected, while if the outcome is tails, then a ball from urn 2 is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails (round up to 2 decimal places)?
  • a)
    0.324
  • b)
    0.28
  • c)
    0.26
  • d)
    0.30
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Urn 1 has five white and seven black balls. Urn 2 has three white and ...
Calculating the probability:
- Let's denote the events as follows:
- A: Coin landed heads
- B: White ball is selected
- We need to find P(A|B), which is the probability that the coin landed tails given that a white ball was selected.

Using Bayes' theorem:
- P(A|B) = P(A and B) / P(B)
- P(A and B) = P(White from Urn 1) * P(Heads) = (5/12) * (1/2) = 5/24
- P(B) = P(White from Urn 1) * P(Heads) + P(White from Urn 2) * P(Tails) = (5/12) * (1/2) + (3/15) * (1/2) = 13/24

Substitute the values:
- P(A|B) = (5/24) / (13/24) = 5/13 ≈ 0.38

Rounding up to 2 decimal places:
- The probability that the coin landed tails given that a white ball was selected is 0.38, which rounds up to 0.32.
Therefore, the correct answer is option A) 0.32.
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Community Answer
Urn 1 has five white and seven black balls. Urn 2 has three white and ...
As we know that,
P (getting tails) = P (getting heads) = 1/2
P (getting white ball from urn 1 ) = P (getting head) × P (white ball from urn 1 )
 = 1/2 × 5/12
P (getting white ball from urn 2) = P (getting tails) ×P (white ball from urn 2)
= 1/2 × 3/15
P (getting white) = P (getting white from urn 1 ) + P (getting white from urn 2 )
= 1/2 × 5/12 + 1/2 × 3/15
= 0.3083
Now, probability that coin landed tails given that ball was white,
P (Coin turns into tails ∣ Ball was white) = 
= 0.324
Hence, the correct option is (A).
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Urn 1 has five white and seven black balls. Urn 2 has three white and twelve black balls. We flip a fair coin. If the outcome is head, then a ball from urn 1 is selected, while if the outcome is tails, then a ball from urn 2 is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails (round up to 2 decimal places)?a)0.324b)0.28c)0.26d)0.30Correct answer is option 'A'. Can you explain this answer?
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Urn 1 has five white and seven black balls. Urn 2 has three white and twelve black balls. We flip a fair coin. If the outcome is head, then a ball from urn 1 is selected, while if the outcome is tails, then a ball from urn 2 is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails (round up to 2 decimal places)?a)0.324b)0.28c)0.26d)0.30Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Urn 1 has five white and seven black balls. Urn 2 has three white and twelve black balls. We flip a fair coin. If the outcome is head, then a ball from urn 1 is selected, while if the outcome is tails, then a ball from urn 2 is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails (round up to 2 decimal places)?a)0.324b)0.28c)0.26d)0.30Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Urn 1 has five white and seven black balls. Urn 2 has three white and twelve black balls. We flip a fair coin. If the outcome is head, then a ball from urn 1 is selected, while if the outcome is tails, then a ball from urn 2 is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails (round up to 2 decimal places)?a)0.324b)0.28c)0.26d)0.30Correct answer is option 'A'. Can you explain this answer?.
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