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 $\frac{0.65}5$.
 A: 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%.
A: You need to check your intuition - how does increasing the number of throws decrease the probability of at least one head (you divide by $5$)?
Another answer has given you the right calculation, but here are some things to think about so that you start noticing the right things here:


*

*As the number of flips increases, the chance of at least one head does not decrease (and in fact increases)

*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 $1$
So if you get an answer, or an intuition, or a result of applying "basic probability", which does not conform to these observations, then something has done wrong with your thinking. That should be a big hint to get you thinking in the right way about the problem.
