Probability of coin toss.

Suppose you flip a fair coin twice. What is the probability of getting two heads in a row (HH)? What about the probability of getting heads followed by tails (HT)?

Are the necessarily the same?

I thought they are necessarily the same because the probability of getting head or tails in a given toss is $\frac{1}{2}$.

So, $\text{P(HH})= \frac{1}{2} \times \frac{1}{2}$

And the same for P(HT)?

• You are correct. They are the same.
– Remy
Commented Oct 29, 2017 at 4:33
• Notice that the question "What is the probability of getting heads, given you got heads last throw" which is also the set {H,H} is actually not the same as asking the probability of flipping two heads in a row. I know this isn't what you asked, but it's something to note if you're starting to learn Probability Theory. Commented Oct 29, 2017 at 4:59

They are the same. The probability of getting heads is $.5$, and the probably of getting tails is $.5$. The two tosses are independent, so the probability of getting heads and then tails is $.5^2$, and so is the probability of getting heads and then heads.
A way to check is if the sum of the probabilities of all the possibilities of flipping a coin twice sums to $1$. $P(HH)=P(HT)=P(TH)=P(TT)=.5^2=.25$ and $4(.25)=1$.
Note that this can generalized. The probability of getting a sequence $HTTHHTHT$ is the same as getting $HHHHHHHH$.
Yes, the possibilities are (HH), (HT), (TH), and (TT). 1 possibility out of four is $1/4$.