Multiple choice

$8$ unbiased coins are tossed at a time $512$ times.The expected frequency of getting one head is

  1. $4$
  2. $8$
  3. $16$
  4. $20$
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C Correct answer
Explanation

Binomial distribution: n=8, p=0.5. Probability of 1 head = 8C1 * (0.5)^1 * (0.5)^7 = 8 * (1/256) = 8/256 = 1/32. Expected frequency = 512 * (1/32) = 16.

AI explanation

Using the binomial distribution expected frequency formula, multiply the number of trials by the probability of exactly one success. The probability of getting exactly one head is 8C1 * (1/2)^8 = 8/256. Multiplying this probability by the 512 total trials gives 16.

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