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 = 5/32. What is the value of n?
A.4
B.5✓ Correct
C.6
D.7
Explanation
p = 1 - P(no tails) = 1 - (1/2)ⁿ. q = 1 - P(0 tails) - P(1 tail) = 1 - (1/2)ⁿ - n(1/2)ⁿ = 1 - (n+1)/2ⁿ. So p - q = (n+1)/2ⁿ - 1/2ⁿ = n/2ⁿ = 5/32. Testing n = 5: 5/32 ✓. So n = 5.
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