If you flip a fair coin four times, what is the probability that you get heads at least twice?
Consider a general task of flipping N coins and the probability of exactly K times the heads are up. Let's use a symbol
Knowing this, we can use the result to evaluate
which will answer the question of what is the probability of getting heads at lease 2 times out of flipping a coin 4 times.
Since there are only
The outcomes we are interested in are those that contain exactly
Any outcome of the random experiment of flipping a coin N times can be represented as a string of N characters, each one being a letter H (to designate that the corresponding flip resulted in a head) or T (if it was a tail).
The number of outcomes with exactly
This number is, obviously, a number of combinations of K items out of N, which symbolically is represented as
For all the theory behind this and other formulas of combinatorics we can refer you to a corresponding part of the advanced course of mathematics for high school at Unizor.
The probability of having
Now we can calculate the probability of at least two heads out of four flips (don't forget that