1992 AHSME Problems/Problem 29

Problem

An "unfair" coin has a $2/3$ probability of turning up heads. If this coin is tossed $50$ times, what is the probability that the total number of heads is even?

$\text{(A) } 25(\frac{2}{3})^{50}\quad \text{(B) } \frac{1}{2}(1-\frac{1}{3^{50}})\quad \text{(C) } \frac{1}{2}\quad \text{(D) } \frac{1}{2}(1+\frac{1}{3^{50}})\quad \text{(E) } \frac{2}{3}$

Solution

$\fbox{D}$

1992 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 28	Followed by Problem 30
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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1992 AHSME Problems/Problem 29

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