$201$ coins each with probability $P(0
- $\dfrac{1}{4}$
- $\dfrac{1}{3}$
- $\dfrac{1}{2}$
- $\dfrac{1}{6}$
Reveal answer
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C
Correct answer
Explanation
For binomial distribution B(n, p), P(X=k) = P(X=k+1) implies nCk * p^k * (1-p)^(n-k) = nC(k+1) * p^(k+1) * (1-p)^(n-k-1). With n=201 and k=100, this simplifies to p = 1-p, so p = 0.5.
AI explanation
Using the binomial probability formula, the probability of getting 100 heads is 201C100 * P^100 * (1-P)^101, and the probability of 101 heads is 201C101 * P^101 * (1-P)^100. Equating the two expressions and simplifying yields 201C100 * (1-P) = 201C101 * P. Since 201C101 = 201C100, the equation simplifies to 1-P = P, making P = 1/2.