Multiple choice

A bag contain 16 coins of which two are counterfeit with heads on both sides.The rest are fair coins. One is selected at random from bag and tossed. The probability of getting a head is

  1. $\dfrac{9}{{16}}$
  2. $\dfrac{11}{{16}}$
  3. $\dfrac{5}{{9}}$

  4. none of these
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A Correct answer
Explanation

There are 16 coins total: 2 are double-headed (probability of head = 1) and 14 are fair (probability of head = 0.5). Total probability = (2/16)*1 + (14/16)*0.5 = 2/16 + 7/16 = 9/16.

AI explanation

By the law of total probability, the chance of getting a head is the sum of the probabilities of drawing a fair coin or a fake coin. The probability is (14/16) * (1/2) + (2/16) * 1. Calculating this gives 7/16 + 2/16, which equals 9/16.

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