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

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

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Answer 1 · 2015-10-22T17:47:31

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

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

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

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

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

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

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