Question

If you flip one coin four times what is the probability of getting at least two tails?

Answer 1

The probability is `11/16=0.6875`.

Explanation:

There are `2^(4)=16` possible outcomes when you flip a coin four times. Of these outcomes, 11 have two or more tails: `{T T T T,T T TH,T T HT,THT T,HT T T,T T HH,T H T H,T HH T,H T T H,H T H T,HH T T}`.

Assuming these outcomes are equally likely (the coin is "fair") gives a probability of `11/16=0.6875`.

In terms of the binomial probability formula with `n=4` and `p=0.5` and `nCr=(n!)/(r! * (n-r)!)`, we have

`P(X geq 2)=1-P(X<2)=1-(P(X=0)+P(X=1))`

`=1 - 4C0 * .5^(0) * .5^4- 4C1 * .5^(1) * .5^3`

`=1-(4!)/(0! * 4!) * 0.0625- (4!)/(1! * 3!) * 0.0625`

`=1-0.0625-4*0.0625=1-0.3125=0.6875`