Question

Three coins are tossed simultaneously. Then the probability that exactly two tails appear is:

• A. \( \frac{1}{8} \)
• B. \( \frac{1}{4} \)
• C. \( \frac{3}{8} \)
• D. \( \frac{1}{2} \)
• E. \( \frac{5}{8} \)

Hint:

For problems involving probability of specific outcomes (such as getting heads or tails), list all possible outcomes and count the favorable ones to determine the probability.

Answer 1

The Correct Option is C

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), \( \frac{3}{8} \).