Question:
Three unbiased coins are tossed. The probability of getting at least 2 tails is:
Three unbiased coins are tossed. The probability of getting at least 2 tails is:
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“At least” means include all cases greater than or equal to the number given.
Updated On: May 1, 2026
- \( \frac{3}{4} \)
- \( \frac{1}{4} \)
- \( \frac{1}{2} \)
- \( \frac{1}{3} \)
- \( \frac{2}{3} \)
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The Correct Option is C
Solution and Explanation
Concept: Probability is given by: \[ P = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} \] For \( n \) coin tosses, total outcomes \( = 2^n \). “At least 2 tails” means outcomes with 2 tails or 3 tails.
Step 1: Find total outcomes.
For 3 coins: \[ \text{Total outcomes} = 2^3 = 8 \] Sample space: \[ \{HHH,\ HHT,\ HTH,\ THH,\ HTT,\ THT,\ TTH,\ TTT\} \]
Step 2: Count favorable outcomes.
Exactly 2 tails: \[ \{HTT,\ THT,\ TTH\} \Rightarrow 3 \text{ outcomes} \] Exactly 3 tails: \[ \{TTT\} \Rightarrow 1 \text{ outcome} \] Total favorable outcomes: \[ 3 + 1 = 4 \]
Step 3: Calculate probability.
\[ P(\text{at least 2 tails}) = \frac{4}{8} \] \[ = \frac{1}{2} \]
Step 4: Final answer.
\[ \boxed{\frac{1}{2}} \]
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