# A coin is weighted so that a head is twice as likely to occur as a tail. The coin is flipped 10 times and the result of each flip is noted. Find the probability that both heads and tails occurs.

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### 1 Answer

The coin is weighted so that a head is twice as likely to occur as a tail.

When the coin is flipped, the probability of getting heads is 2/3 and the probability of getting tails is 1/3.

If the coin is flipped 10 times, the probability that both heads and tails occurs is equal to 1 - (probability that only heads occurs) - (probability that only tails occurs) = `1 - (2/3)^10 - (1/3)^10 ~~ 0.9826`

**The required probability that both heads and tails occurs is approximately 0.9826**