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

1 Answer
Bill K.
Oct 22, 2015

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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