If you flip a coin 3 times, what is the probability of flipping heads 3 times?

Answer:12.5% probability of flipping heads 3 times.Step-by-step explanation:For each coin, there are only two possible outcomes. Either it is heads, or it is tails. The probabilitis for each coin are also independent. So we use the binomial probability distribution to solve this problem.Binomial probability distributionThe binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]And p is the probability of X happening.In this problem we have that:In each coin toss, heads or tails are equally as likely. So [tex]p = \frac{1}{2} = 0.5}[/tex]If you flip a coin 3 times, what is the probability of flipping heads 3 times?This is P(X = 3) when n = 3. So[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex][tex]P(X = 3) = C_{3,3}.(0.5)^{3}.(0.5)^{0} = 0.125[/tex]12.5% probability of flipping heads 3 times.