What is the value of n?
Consider the following for the next two (02) items that follow : An unbiased coin is tossed n times. The probability of getting at least one tail is p and the probability of at least two tails is q and p-q=\frac{5}{32}.
- A. 4
- B. 5 ✓
- C. 6
- D. 7
Correct Answer: B. 5
Explanation
Let X be the number of tails, following a Binomial distribution B(n, 1/2). p = P(X \geq 1) = 1 - P(X=0) and q = P(X \geq 2) = 1 - P(X=0) - P(X=1). The difference is p - q = P(X=1) = \binom{n}{1}(\frac{1}{2})^n = \frac{n}{2^n}. We are given \frac{n}{2^n} = \frac{5}{32}. By inspection, setting n=5 yields \frac{5}{2^5} = \frac{5}{32}, which holds true.
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