What is the probability of getting two heads when flipping a fair coin twice?

• A. 1/2
• B. 1/8
• C. 3/4
• D. 1/4

Answer: (D)

Flipping a fair coin twice involves two independent trials, each with two equally likely outcomes: heads or tails. To get two heads, both flips must be heads. The probability of the first flip being heads is 1/2, and the probability of the second being heads is also 1/2; since the flips are independent, multiply them: 1/2 × 1/2 = 1/4. Another way to see it is that there are four equally likely outcomes (HH, HT, TH, TT), and only one of them is two heads, so the probability is 1 out of 4, which is 1/4. The other numbers don’t match the event of two heads in two flips: 1/2 is a single-flip probability, 3/4 is the complement of not getting two heads, and 1/8 corresponds to something involving three flips. So the probability is 1/4.