Multiple choice

Denomination, one of the coins is known to have heads. He takes out one coin at random and tosses it 5 times. If it always falls with head upwards,the probability that it is double-headed coin is

  1. $\displaystyle \frac{32}{51}$
  2. $\displaystyle \frac{32}{41}$
  3. $\displaystyle \frac{32}{61}$
  4. $\displaystyle \frac{12}{41}$
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B Correct answer
AI explanation

Using Bayes' theorem, the prior probability of selecting the double-headed coin is 1/2, and the probability of getting five heads is 1. The prior probability of selecting the fair coin is 1/2, and the probability of getting five heads is 1/32. The posterior probability is (1/2 * 1) divided by the sum of (1/2 * 1) and (1/2 * 1/32), which simplifies to 32/41.

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