If three unbiased coins are tossed, find the probability that they are all heads

Analyze the question: Three fair coins are tossed. We want the probability that all three show heads.

Concept: Each toss is independent, so we multiply the probabilities of each outcome. For an unbiased coin, P(Head) = ½.

Solution:

Method 1: Multiplication rule

P(HHH) = P(H) × P(H) × P(H) = ½ × ½ × ½ = 1/8

Method 2: Sample space

Each coin has 2 outcomes, so the total number of outcomes is 2³ = 8: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

Only 1 of these is HHH, so the probability is 1/8.

Checking the options:

• A (½) is the probability for a single head.
• B (⅓) and C (1/9) don't match any coin-toss calculation here.
• D (1/8) matches our working.

Answer: D (1/8)

Tip: For n coin tosses, the total number of outcomes is 2ⁿ, and the probability of any one specific sequence (such as all heads) is 1/2ⁿ. For 2 coins it's 1/4, for 3 coins 1/8, and for 4 coins 1/16.