Multiple choice

A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n - 3) is

  1. 2-1

  2. 0

  3. nCn-3 2-n

  4. 2-n+3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let H be the number of heads and T be the number of tails. H + T = n and H - T = n - 3. Adding these, 2H = 2n - 3, so H = n - 1.5. Since H must be an integer, there is no possible outcome where the difference is n - 3. Thus, the probability is 0.

AI explanation

The difference between the number of heads and tails after n tosses has the same parity (even or odd nature) as n. For the difference to equal (n - 3), the value (n - 3) must have the same parity as n. Since 3 is an odd number, n and (n - 3) will always have opposite parities, making the condition mathematically impossible to achieve. Therefore, the probability is 0.

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