Multiple choice

The probability of obtaining more tails than heads in $6$ tosses of a fair coins is?

  1. $2/64$
  2. $22/64$
  3. $21/64$

  4. None
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B Correct answer
Explanation

In 6 tosses, the total outcomes are 2^6 = 64. The probability of more tails than heads is the same as the probability of more heads than tails, and since the probability of equal heads and tails (3 each) is (6C3)/64 = 20/64, the remaining 44 outcomes are split equally between more heads and more tails, giving 22/64 each.

AI explanation

To find the probability of obtaining more tails than heads in 6 tosses of a fair coin, we sum the probabilities of getting exactly 4, 5, and 6 tails. Using the binomial distribution formula, the probability for 4 tails is 6C4 times (1/2)^6, for 5 tails is 6C5 times (1/2)^6, and for 6 tails is 6C6 times (1/2)^6. This gives (15 + 6 + 1) divided by 64, which equals 22/64.

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