Multiple choice

If a coin is tossed a fixed number of times, the probability of getting 6 heads is equal to the probability of getting 8 heads. Find the number of times the coin was tossed.

  1. $12$
  2. $13$
  3. $14$
  4. $15$
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C Correct answer
Explanation

In a binomial distribution, P(X=k) = P(X=n-k) if the probability of success is 0.5. Here, 6 + 8 = 14, so the total number of tosses n = 14.

AI explanation

According to the properties of the binomial distribution, the probability of getting k successes in n trials is equal to the probability of getting n minus k successes. Given that the probability of getting 6 heads equals the probability of getting 8 heads, we set n minus 6 equal to 8. Solving this equation gives a total of 14 tosses.

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