# Calculate chance of getting heads from weighted coin after 5 trials

Let's say I have a coin weighted toward heads – 65% heads. What's the chance I will get at least one head if I have to flip the coin 5 times?

Basic probability and intuition tells me $$\frac{0.65}5$$.

The answer is not $$\frac{65}5$$, $$\frac{0.65}5$$ or similar things to those. To get the correct answer: there is a 0.35 chance of getting tails, so the probability that you get five tails and no heads is $$0.35^5$$. The complement probability, that of getting some head in five tosses, is the complement of this, or $$1-0.35^5=0.9947$$ – i.e. around 99.5%.
You need to check your intuition - how does increasing the number of throws decrease the probability of at least one head (you divide by $$5$$)?
2. It is always possible, though increasingly unlikely as the number of flips increases, that all the flips will be tails, so the probability of at least one head is never equal to $$1$$