Question

A fair coin is flipped four times. Find the probability that at least two of the flips will turn up as heads.

Answer 1

the probability of having K heads out of N flips can be found with the formula:

`P(N,K)\text{ = }(C^K_N)/(2^N)`

the 2 comes from having only two possible outcomes!

So, we need to find P(4,2) + P(4,3) + P(4,4):

`\begin{gathered} P\mleft(4,2\mright)+P\mleft(4,3\mright)+P\mleft(4,4\mright)\text{ = }(1)/(2^4)\cdot\text{(}(4!)/(2!\cdot2!)\text{ + }(4!)/(3!)+\text{ }(4!)/(4!)\text{ ) } \\ =\text{ }(6+4+1)/(16)\text{ = }0.6875 \end{gathered}`