Question

Three coins are tossed together. The probability that at least one head comes up is

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

Hint:

To find the probability of "at least one", subtract the probability of "none" from 1.

Answer 1

The Correct Option is B

Problem:
Three coins are flipped simultaneously.
Determine the probability of obtaining at least one head.

Step 1: Determine all possible outcomes
Each coin has two outcomes: heads or tails.
Total outcomes for three coins: \(2^3 = 8\).

Step 2: Calculate the probability of the complement (no heads)
"No heads" is equivalent to all tails.
Number of ways to get all tails = 1 (TTT)
Probability of no heads = \(\frac{1}{8}\).

Step 3: Compute the desired probability
Probability of at least one head = \(1 - \text{Probability of no heads}\)
\[= 1 - \frac{1}{8} = \frac{7}{8}\]

Solution:
\[\boxed{\frac{7}{8}}\]