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1992 AMC 12 Question 29

AMC12 · 1992 AMC 12

Question 29

An “unfair” coin has a $\frac23$ probability of turning up heads. If this coin is tossed $50$ times, what is the probability that the total number of heads is even?
  1. $2^5\left(\frac23\right)^{50}$
  2. $\frac12\left(1-\frac1{3^{50}}\right)$
  3. $\frac12$
  4. $\frac12\left(1+\frac1{3^{50}}\right)$
  5. $\frac23$