# Possible outcomes on a three coin flip. [closed]

If you flip a coin three times, the possible outcomes are $\left \lbrace HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \right \rbrace$ What is the probability of getting two tails?

## closed as off-topic by Adam Hughes, Juniven, Claude Leibovici, JonMark Perry, zhorasterFeb 24 '17 at 9:15

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• Any Work to show ? – Vivek Kaushik Feb 24 '17 at 4:57
• Um, how many of those have two tails? You listed them all. Do you know how to count? – fleablood Feb 24 '17 at 6:08

Clearly you can see cases with two tails are HTT, THT, TTH = 3 cases.

And total cases are 8.

So probability = $\frac 38$

Using binomial probability formula: $p$(k successes in n trials) = $\binom{n}{k}p^{k}q^{n-k}$

In this case $p=q=0.5$, $n = 3$, $k = 2$

Then we get $p$(k successes in n trials) = $\binom{3}{2}0.5^{2}*0.5$ = $\frac{3}{8}$

Alternatively since $n$ is small, you could draw a probability tree diagram and solve it that way.

Hint:

Just count the number of cases in the sample space where there are two tails. On a side note, it would be easier if you used combinations. The ways to select two tails from a possible three equal: $\binom {3}{2}=3$ where $\binom{n}{k}$ is the binomial coefficient. Then you can easily calculate the probability.

Hope it helps.