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If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?
  • a)
    1/3
  • b)
    1/4
  • c)
    1/2
  • d)
    2/3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If two fair coins are flipped and at least one of the outcomes is know...
Sample space = {HH, HT, TH}
Required probability = 1/3
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Most Upvoted Answer
If two fair coins are flipped and at least one of the outcomes is know...
Understanding the Problem
When flipping two fair coins, we have four possible outcomes:
- HH (both heads)
- HT (first head, second tail)
- TH (first tail, second head)
- TT (both tails)
Since we are told that at least one of the outcomes is a head, we can eliminate the outcome TT.
Remaining Outcomes
After removing TT, the remaining outcomes are:
- HH
- HT
- TH
This gives us a total of three equally likely outcomes.
Identifying Favorable Outcomes
Now, we want to find the probability that both coins show heads (HH) given that at least one coin is a head. The favorable outcome we are interested in is HH.
Calculating Probability
To calculate the probability, we use the formula:
Probability = (Number of favorable outcomes) / (Total outcomes after applying the condition)
- Number of favorable outcomes (HH) = 1
- Total outcomes (HH, HT, TH) = 3
Thus, the probability is:
Probability = 1/3
Conclusion
Therefore, the probability that both outcomes are heads, given that at least one coin shows heads, is:
Answer: 1/3 (Option A)
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