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An unbiased coin is tossed three times. The probability that the head turns up in exactly two cases is
- a)1/9
- b)1/8
- c)2/3
- d)3/8
Correct answer is option 'D'. Can you explain this answer?
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An unbiased coin is tossed three times. The probability that the head ...
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An unbiased coin is tossed three times. The probability that the head ...
Understanding the Problem
When tossing an unbiased coin three times, we want to determine the probability of getting exactly two heads.
Possible Outcomes
For three tosses, the sample space consists of:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH
- TTT
This results in a total of 2^3 = 8 possible outcomes.
Favorable Outcomes
To find the favorable outcomes where exactly two heads appear, we can list them:
- HHT
- HTH
- THH
There are 3 favorable outcomes.
Calculating the Probability
The probability of an event is calculated using the formula:
Probability = (Number of Favorable Outcomes) / (Total Outcomes)
In this case:
- Number of Favorable Outcomes = 3
- Total Outcomes = 8
Thus, the probability of getting exactly two heads is:
Probability = 3 / 8
Conclusion
The correct answer to the probability of getting heads exactly two times when tossing a coin three times is:
- Probability = 3/8
Hence, the correct option is D.
When tossing an unbiased coin three times, we want to determine the probability of getting exactly two heads.
Possible Outcomes
For three tosses, the sample space consists of:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH
- TTT
This results in a total of 2^3 = 8 possible outcomes.
Favorable Outcomes
To find the favorable outcomes where exactly two heads appear, we can list them:
- HHT
- HTH
- THH
There are 3 favorable outcomes.
Calculating the Probability
The probability of an event is calculated using the formula:
Probability = (Number of Favorable Outcomes) / (Total Outcomes)
In this case:
- Number of Favorable Outcomes = 3
- Total Outcomes = 8
Thus, the probability of getting exactly two heads is:
Probability = 3 / 8
Conclusion
The correct answer to the probability of getting heads exactly two times when tossing a coin three times is:
- Probability = 3/8
Hence, the correct option is D.
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