The Math Meridian
Back to Counting and Combinatorics

Coin-toss probability with Pascal's triangle

Questions at easy, medium and hard levels. Pick a level and get a fresh set every time, with instant feedback.

Learn it When n fair coins are tossed, there are 2ⁿ equally likely outcomes. Row n of Pascal's triangle (starting with row 0 at the top) counts them: the (k + 1)th number tells how many ways to get exactly k heads, which is nCk. So P(exactly k heads) = nCk ÷ 2ⁿ.

Example: Four coins are tossed. Find the probability of exactly 2 heads.

  1. Row 4 of Pascal's triangle: 1, 4, 6, 4, 1. They add to 2⁴ = 16.
  2. Exactly 2 heads is the third number: 6.
  3. P = 6/16 = 3/8.

Loading questions…