Multiple choice

What is the possibility of getting at least 6 heads if eight coins are tossed simultaneously?

  1. $\dfrac{37}{256}$
  2. $\dfrac{25}{57}$
  3. $\dfrac{1}{13}$
  4. $\dfrac{5}{27}$
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A Correct answer
Explanation

Total outcomes = 2^8 = 256. At least 6 heads means 6, 7, or 8 heads. Number of ways = C(8,6) + C(8,7) + C(8,8) = 28 + 8 + 1 = 37. Probability = 37/256.

AI explanation

To find the probability of getting at least 6 heads when eight coins are tossed, we use the binomial distribution formula P(X = k) = nCr * (1/2)^n. The favorable outcomes are getting exactly 6, 7, or 8 heads, which is calculated as (8C6 + 8C7 + 8C8) outcomes. This gives (28 + 8 + 1) / 2^8, equaling 37 out of 256 total possible outcomes. The probability is 37/256.

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