If you flip a coin three times, what is the probability of getting tails three times?

1 Answer

#1/8#

Explanation:

To calculate the probability you have to name all possible results first. If you mark a result of a single coin flip as #H# for heads or #T# for tails all results of #3# flips can be written as:

#Omega={(H,H,H),(H,H,T),(H,T,H),(H,T,T),(T,H,H),(T,H,T),(T,T,H),(T,T,T)}#

Each triplet contains results on #1#st, #2#nd and #3#rd coin. So you can see that in total there are #8# elementary events in #Omega#.

#|Omega|=8#

Now we have to define event #A# of getting tails three times.

The only elementary event which satisfies this condition is #(T,T,T)# so we can write that:

#A={(T,T,T)}#
#|A|=1#

Now according to the (classic) definition of probability we can write, that:

#P(A)=|A|/|Omega|=1/8#

So finally we can write the answer:

Probability of getting 3 tails in 3 coin flips is #1/8#.