Multiple choice

Three coins are tossed. Two of them are fair and one is biased so that a head is three times as likely as a tail. Find the probability of getting two heads and a tail

  1. $\displaystyle \frac {7}{16}$
  2. $\displaystyle \frac {3}{4}$
  3. $\displaystyle \frac {9}{16}$
  4. $\displaystyle \frac {1}{2}$
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A Correct answer
AI explanation

For the biased coin, the probability of a head is 3/4 and the probability of a tail is 1/4. The total probability of getting two heads and one tail is the sum of three mutually exclusive cases: (1/2)(1/2)(1/4) + (1/2)(1/4)(1/2) + (3/4)(1/2)(1/2). Adding these probabilities gives 1/16 + 1/16 + 3/16, which equals 7/16. The result is 7/16.

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