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There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs all 4 times, then the probability that the false coin has been chosen for tossing is ___.
- a)0.82
- b)0.87
Correct answer is between '0.82,0.87'. Can you explain this answer?
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Verified Answer
There are 3 fair coins and 1 false coin with tails on both sides. A c...
Required Probability = Favorable Outcomes / Total possible outcomes
View all questions of this test
Favourable outcomes = A false coin is chosen and flipped every time Probability of selecting a false coin =1/4 Probability of getting a tail on every flip of false coin =1. Favourable outcome
= 1/4 × 1 = 1/4
Total possible outcomes = Favourable outcomes + Unfavorable outcomes Unfavorable outcomes = A fair coin is chosen and flipped every time to get tail Probability of selecting a fair coin = 3/4 Probability of flipping a fair coin 4 times and getting tails every time
= (1/2)4 = 116 ∴ Unfavourable outcomes
= 3/4 × 1/16 = 3/64
Total possible outcomes
= 1/4 + 3/64 = 19/64
∴ Required probability
= 
= 16/19
= 0.84
Most Upvoted Answer
There are 3 fair coins and 1 false coin with tails on both sides. A c...
Solution:
Given,
Number of fair coins=3
Number of false coins=1
A coin is chosen at random and tossed 4 times
Let's assume the events as follows,
E1: Choosing a fair coin
E2: Choosing a false coin
F: Getting tails all four times
We need to find the probability of the false coin being chosen given that tails occurred all four times. That is P(E2/F).
Using Bayes' theorem we have,
P(E2/F) = P(F/E2) * P(E2) / [P(F/E2) * P(E2) + P(F/E1) * P(E1)]
where,
P(E1) = Probability of choosing a fair coin = 3/4
P(E2) = Probability of choosing a false coin = 1/4
P(F/E1) = Probability of getting tails all four times given a fair coin is chosen = (1/2)^4 = 1/16
P(F/E2) = Probability of getting tails all four times given a false coin is chosen = 1
Substituting the values we get,
P(E2/F) = 1 * 1/4 / [1 * 1/4 + 1/16 * 3/4]
= 4/5 = 0.8
Therefore, the probability that the false coin has been chosen for tossing when tails occurs all 4 times is 0.8 or 0.82 (rounded to two decimal places) which is between the given options (0.82, 0.87).
Given,
Number of fair coins=3
Number of false coins=1
A coin is chosen at random and tossed 4 times
Let's assume the events as follows,
E1: Choosing a fair coin
E2: Choosing a false coin
F: Getting tails all four times
We need to find the probability of the false coin being chosen given that tails occurred all four times. That is P(E2/F).
Using Bayes' theorem we have,
P(E2/F) = P(F/E2) * P(E2) / [P(F/E2) * P(E2) + P(F/E1) * P(E1)]
where,
P(E1) = Probability of choosing a fair coin = 3/4
P(E2) = Probability of choosing a false coin = 1/4
P(F/E1) = Probability of getting tails all four times given a fair coin is chosen = (1/2)^4 = 1/16
P(F/E2) = Probability of getting tails all four times given a false coin is chosen = 1
Substituting the values we get,
P(E2/F) = 1 * 1/4 / [1 * 1/4 + 1/16 * 3/4]
= 4/5 = 0.8
Therefore, the probability that the false coin has been chosen for tossing when tails occurs all 4 times is 0.8 or 0.82 (rounded to two decimal places) which is between the given options (0.82, 0.87).
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There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs all 4 times, then the probability that the false coin has been chosen for tossing is ___.a)0.82b)0.87Correct answer is between '0.82,0.87'. Can you explain this answer?
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There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs all 4 times, then the probability that the false coin has been chosen for tossing is ___.a)0.82b)0.87Correct answer is between '0.82,0.87'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs all 4 times, then the probability that the false coin has been chosen for tossing is ___.a)0.82b)0.87Correct answer is between '0.82,0.87'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs all 4 times, then the probability that the false coin has been chosen for tossing is ___.a)0.82b)0.87Correct answer is between '0.82,0.87'. Can you explain this answer?.
There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs all 4 times, then the probability that the false coin has been chosen for tossing is ___.a)0.82b)0.87Correct answer is between '0.82,0.87'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs all 4 times, then the probability that the false coin has been chosen for tossing is ___.a)0.82b)0.87Correct answer is between '0.82,0.87'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs all 4 times, then the probability that the false coin has been chosen for tossing is ___.a)0.82b)0.87Correct answer is between '0.82,0.87'. Can you explain this answer?.
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