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A coin is tossed until a heard appears or until the coin has been tossed 5 times. If a head does not occur on the first two losses, then the probability that the coin will be tossed 5 times is
- a)1/6
- b)1/8
- c)1/12
- d)none of the above
Correct answer is option 'D'. Can you explain this answer?
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A coin is tossed until a heard appears or until the coin has been toss...
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Problem:
A coin is tossed until a head appears or until the coin has been tossed 5 times. If a head does not occur on the first two tosses, then what is the probability that the coin will be tossed 5 times?
Solution:
To find the probability that the coin will be tossed 5 times, we need to analyze the possible outcomes and count the favorable outcomes.
Possible Outcomes:
When tossing a coin, there are two possible outcomes: heads (H) or tails (T).
Analysis:
Let's analyze the possible scenarios when the coin is tossed:
1. The head appears on the first toss (H):
- The coin is tossed only once.
2. The head appears on the second toss (TH):
- The coin is tossed twice.
3. The head appears on the third toss (TTH):
- The coin is tossed three times.
4. The head appears on the fourth toss (TTTH):
- The coin is tossed four times.
5. The head appears on the fifth toss (TTTTH):
- The coin is tossed five times.
Counting Favorable Outcomes:
From the above analysis, we can observe that the favorable outcomes are when the head appears on the fifth toss (TTTTH). There is only one favorable outcome.
Counting Total Outcomes:
To count the total outcomes, we need to consider all the possible scenarios. From the analysis, we can see that there are five possible scenarios (H, TH, TTH, TTTH, TTTTH).
Probability:
The probability is equal to the number of favorable outcomes divided by the number of total outcomes.
Number of favorable outcomes = 1
Number of total outcomes = 5
Therefore, the probability that the coin will be tossed 5 times is 1/5.
Final Answer:
The correct answer is Option D: none of the above because none of the given options match the probability we calculated.
A coin is tossed until a head appears or until the coin has been tossed 5 times. If a head does not occur on the first two tosses, then what is the probability that the coin will be tossed 5 times?
Solution:
To find the probability that the coin will be tossed 5 times, we need to analyze the possible outcomes and count the favorable outcomes.
Possible Outcomes:
When tossing a coin, there are two possible outcomes: heads (H) or tails (T).
Analysis:
Let's analyze the possible scenarios when the coin is tossed:
1. The head appears on the first toss (H):
- The coin is tossed only once.
2. The head appears on the second toss (TH):
- The coin is tossed twice.
3. The head appears on the third toss (TTH):
- The coin is tossed three times.
4. The head appears on the fourth toss (TTTH):
- The coin is tossed four times.
5. The head appears on the fifth toss (TTTTH):
- The coin is tossed five times.
Counting Favorable Outcomes:
From the above analysis, we can observe that the favorable outcomes are when the head appears on the fifth toss (TTTTH). There is only one favorable outcome.
Counting Total Outcomes:
To count the total outcomes, we need to consider all the possible scenarios. From the analysis, we can see that there are five possible scenarios (H, TH, TTH, TTTH, TTTTH).
Probability:
The probability is equal to the number of favorable outcomes divided by the number of total outcomes.
Number of favorable outcomes = 1
Number of total outcomes = 5
Therefore, the probability that the coin will be tossed 5 times is 1/5.
Final Answer:
The correct answer is Option D: none of the above because none of the given options match the probability we calculated.
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A coin is tossed until a heard appears or until the coin has been tossed 5 times. If a head does not occur on the first two losses, then the probability that the coin will be tossed 5 times isa)1/6b)1/8c)1/12d)none of the aboveCorrect answer is option 'D'. Can you explain this answer?
Question Description
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