Three coins are tossed simultaneously. Then the probability that exactly two tails appear is:
Show Hint
- \( \frac{1}{8} \)
- \( \frac{1}{4} \)
- \( \frac{3}{8} \)
- \( \frac{1}{2} \)
- \( \frac{5}{8} \)
The Correct Option is C
Solution and Explanation
When three coins are tossed, the total number of possible outcomes is:
\[ 2 \times 2 \times 2 = 8 \]
The possible outcomes are:
\[ \{ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \} \]
where \( H \) represents heads and \( T \) represents tails. We are asked to find the probability that exactly two tails appear.
From the list of outcomes, the favorable outcomes with exactly two tails are:
\[ \{ HTT, THT, TTH \} \]
There are 3 such favorable outcomes.
The probability of getting exactly two tails is given by:
\[ P(\text{exactly 2 tails}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{8} \]
Thus, the correct answer is option (C), \( \frac{3}{8} \).
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