Multiple choice

Two coins are tossed. What is the conditional probability that two heads result, given that there is at least one head ?

  1. $\displaystyle \frac{1}{4}$
  2. $\displaystyle \frac{2}{3}$
  3. $\displaystyle \frac{1}{3}$
  4. $\displaystyle \frac{3}{4}$
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C Correct answer
Explanation

Sample space S = {HH, HT, TH, TT}. Given at least one head, the reduced sample space is {HH, HT, TH}. The event of two heads is {HH}. Probability = 1/3.

AI explanation

Using the conditional probability formula, we find the probability of getting at least one head, which is 3/4 since the outcomes are HH, HT, TH, and TT. The probability of getting two heads (HH) is 1/4. We divide the probability of two heads by the probability of at least one head to get (1/4) divided by (3/4), which equals 1/3.

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