A fair coin is tossed twice. What is the probability of getting heads on both tosses?

Introduction / Context:Independent trials with a fair coin lead to a product rule for probabilities: multiply the probabilities of independent events to get the probability of their joint occurrence.

Given Data / Assumptions:

• Coin is fair: P(H) = 1/2, P(T) = 1/2.
• Two independent tosses.

Concept / Approach:P(H on toss 1 and H on toss 2) = P(H) * P(H) because tosses are independent.

Step-by-Step Solution:P = (1/2) * (1/2) = 1/4.

Verification / Alternative check:Enumerate outcomes: {HH, HT, TH, TT}. Exactly one outcome (HH) out of four gives two heads → 1/4.

Why Other Options Are Wrong:1/2 is for “at least one head” in two tosses (not exactly both); 3/4 is “not both tails”.

Common Pitfalls:Adding probabilities instead of multiplying for independent joint events.

Final Answer:1/4