Multiple choice

South African cricket captain lost the toss of a coin $13$ times out of $14$. The change of this happening was?

  1. $\dfrac{7}{(2^{13})}$
  2. $\dfrac{1}{(2^{13})}$
  3. $\dfrac{13}{(2^{14})}$
  4. $\dfrac{13}{(2^{13})}$
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A Correct answer
Explanation

The probability of losing a toss is 1/2. The probability of losing 13 times out of 14 is C(14, 13) * (1/2)^13 * (1/2)^1 = 14 * (1/2)^14 = 7 * (1/2)^13.

AI explanation

Assuming a fair coin, the probability of losing the toss is 1/2. The probability of losing exactly 13 times out of 14 tosses is found using the binomial distribution formula nCr times p^r times q^(n-r). Substituting the values gives 14C13 times (1/2)^13 times (1/2)^1, which simplifies to 14 times (1/2)^14, or 14 divided by 16384. This simplifies to 7 divided by 2^13, resulting in 7/(2^13).

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