Multiple choice

Twenty coins each with probability $P(0

  1. $\dfrac{9}{20}$
  2. $\dfrac{11}{20}$
  3. $\dfrac{11}{21}$
  4. $\dfrac{9}{21}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the binomial probability formula P(X=k) = C(n, k) * p^k * (1-p)^(n-k), we set C(20, 10) * p^10 * (1-p)^10 = C(20, 11) * p^11 * (1-p)^9. Simplifying gives C(20, 10) * (1-p) = C(20, 11) * p. Since C(20, 11) = C(20, 9), we get (1-p)/p = C(20, 11)/C(20, 10) = 10/11. Solving for p yields p = 11/21.

AI explanation

Using the binomial probability formula, the probability of 10 heads is 20C10 * P^10 * (1-P)^10, and the probability of 11 heads is 20C11 * P^11 * (1-P)^9. Setting these equal and simplifying gives 20C10 * (1-P) = 21C10 * P. Solving this equation using the relationship 20C10 = 20!/(10!10!) and 21C10 = 21!/(10!11!) yields P = 11/21.

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