Question

Three unbiased coins are tossed. Then, the probability of getting at most two heads is:

• A. \(\frac{3}{4}\)
• B. \(\frac{1}{4}\)
• C. \(\frac{3}{8}\)
• D. \(\frac{7}{8}\)

Hint:

“At most two heads” means all cases except getting three heads. Sometimes using the complement is faster.

Answer 1

The Correct Option is D

Step 1: Count the total possible outcomes.
Tossing three coins yields 2³ = 8 equally likely outcomes.

Step 2: Interpret "at most two heads".
This condition permits 0, 1, or 2 heads. The only excluded case is obtaining all three heads (HHH).

Step 3: Compute the favorable outcomes.
Favorable outcomes = Total outcomes - Unfavorable outcome = 8 - 1 = 7.

Step 4: Calculate the probability.
P(at most two heads) = 7/8.

Step 5: Final conclusion.
The probability is 7/8.