What have you learned? Well, to flip a coin n times one for k small or equal to n.
We ask the probability--what are the chance it comes up heads k times.
For any coin, with the probability of heads equals to all caps P,.
we now get the following formula: n!/(n-k)!*k!.
These are the total number of outcomes that have this property.
And then this one has the following probability:
P to the k, this was the (0.8)⁹ before times (1-p) to the n-k,
which is the remaining 3 over here in this example.
So, this formula is the probability of what's call the binomial distribution
and really was this is the accumulated outcome of many identical coin flips,
and it leads us beautifully to our next lesson
when we talk about very large experiments and the normal distribution.
What you should have learned and understand now is you can take very large experiments
with large numbers of coin flips and compute the probability that heads comes a certain number
of times using the formula that you should now fully and wholly understand.