Multiple choice

A fair coin is tossed 𝑛 times. If the probability of getting six heads is equal to the probability of getting eight heads, which of the following gives the value of 𝑛?

  1. 12

  2. 14

  3. 15

  4. 16
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B Correct answer
Explanation

The probability of k successes in n trials is C(n, k) * (1/2)^n. Setting C(n, 6) = C(n, 8) implies n = 6 + 8 = 14, because C(n, k) = C(n, n-k).

AI explanation

For a binomial distribution, the probability of getting k heads in n tosses is given by nCk times p to the power of k times q to the power of (n minus k). Since nC6 equals nC8, we apply the combination property nCr equals nC(n minus r) to write 6 equals n minus 8. Solving this equation yields n equals 14.

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