You can put this solution on YOUR website!
The probability of successes in trials where is the probability of success on any given trial is given by:
Where is the number of combinations of things taken at a time and is calculated by
Your problem is that you want the probability of "at most 4" tails in 5 flips. That means you need to calculate the probability of 0 tails in 5 flips and add that to the probability of 1 tail in 5 flips, 2 tails in 5...you get the picture. Each flip has a probability of 0.5 for a tail, so your calculation will look like this:
Which calculation is guaranteed to provide all the entertainment value that can be obtained watching paint dry.
But all is not lost. Notice that the only alternative to "at most 4 tails" in 5 flips is all 5 of the flips coming up tails. That means we can simply find the probability of 5 tails out of 5 flips and subtract from 1 to get our answer.
And this looks MUCH better, particularly when you realize that and , so really this reduces to:
John
My calculator said it, I believe it, that settles it
