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A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-
- a)2/9
- b)1/9
- c)2/27
- d)1/27
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A coin is based so that a head is twice as likely to occur as a tail. ...
Let probability of tail is 1/3
⇒ Probability of getting head =2/3
∴ Probability of getting 2 tails and 1 head
Most Upvoted Answer
A coin is based so that a head is twice as likely to occur as a tail. ...
Understanding the Coin Bias
The coin is biased such that heads (H) are twice as likely to occur as tails (T). This means the probabilities are:
- Probability of getting a head (P(H)) = 2/3
- Probability of getting a tail (P(T)) = 1/3
Calculating the Probability of 2 Tails and 1 Head
When tossing the coin 3 times, we need to find the probability of getting exactly 2 tails and 1 head.
Possible Outcomes
The possible sequences for getting 2 tails and 1 head are:
- TTH
- THT
- HTT
Calculating Individual Probabilities
For each of these sequences, the probability can be calculated as follows:
- Probability of TTH = P(T) * P(T) * P(H) = (1/3) * (1/3) * (2/3) = 2/27
- Probability of THT = P(T) * P(H) * P(T) = (1/3) * (2/3) * (1/3) = 2/27
- Probability of HTT = P(H) * P(T) * P(T) = (2/3) * (1/3) * (1/3) = 2/27
Total Probability
Now, add the probabilities of all three sequences:
- Total Probability = P(TTH) + P(THT) + P(HTT)
- Total Probability = 2/27 + 2/27 + 2/27 = 6/27 = 2/9
Conclusion
Therefore, the probability of getting exactly 2 tails and 1 head when tossing the biased coin three times is 2/9. The correct answer is option 'A'.
The coin is biased such that heads (H) are twice as likely to occur as tails (T). This means the probabilities are:
- Probability of getting a head (P(H)) = 2/3
- Probability of getting a tail (P(T)) = 1/3
Calculating the Probability of 2 Tails and 1 Head
When tossing the coin 3 times, we need to find the probability of getting exactly 2 tails and 1 head.
Possible Outcomes
The possible sequences for getting 2 tails and 1 head are:
- TTH
- THT
- HTT
Calculating Individual Probabilities
For each of these sequences, the probability can be calculated as follows:
- Probability of TTH = P(T) * P(T) * P(H) = (1/3) * (1/3) * (2/3) = 2/27
- Probability of THT = P(T) * P(H) * P(T) = (1/3) * (2/3) * (1/3) = 2/27
- Probability of HTT = P(H) * P(T) * P(T) = (2/3) * (1/3) * (1/3) = 2/27
Total Probability
Now, add the probabilities of all three sequences:
- Total Probability = P(TTH) + P(THT) + P(HTT)
- Total Probability = 2/27 + 2/27 + 2/27 = 6/27 = 2/9
Conclusion
Therefore, the probability of getting exactly 2 tails and 1 head when tossing the biased coin three times is 2/9. The correct answer is option 'A'.
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A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-a)2/9b)1/9c)2/27d)1/27Correct answer is option 'A'. Can you explain this answer?
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A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-a)2/9b)1/9c)2/27d)1/27Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-a)2/9b)1/9c)2/27d)1/27Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-a)2/9b)1/9c)2/27d)1/27Correct answer is option 'A'. Can you explain this answer?.
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