Question:
Three unbiased coins are tossed. Provided that at least two outcomes are tails, the probability of having all three outcomes as tails is
Three unbiased coins are tossed. Provided that at least two outcomes are tails, the probability of having all three outcomes as tails is
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When calculating conditional probabilities, first identify the restricted sample space and then compute the probability within that space.
Updated On: Sep 4, 2025
- $\dfrac{1}{8}$
- $\dfrac{1}{4}$
- $\dfrac{1}{3}$
- $\dfrac{1}{2}$
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The Correct Option is B
Solution and Explanation
The sample space for tossing 3 unbiased coins is:
\[
\{TTT, TTH, THT, HTT, HHT, HTH, THH, HHH\}
\]
Given that at least two outcomes are tails, the possible outcomes are:
\[
\{TTT, TTH, THT, HTT\}
\]
Thus, the probability of getting all tails ($TTT$) given that at least two tails appear is:
\[
P(\text{All tails} \mid \text{At least two tails}) = \dfrac{1}{4}
\]
Thus, the correct answer is (B) $\dfrac{1}{4}$.
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