Flipping two coins, which is more probable? When flipping two coins, is it more probable for the two coins to match (ex. Heads, Heads) or be different (ex. Heads, Tails).
 A: If the two coins are both fair, there are four equally likely outcomes: $$\{HH, HT, TH, TT\}$$
Of these, in two cases they match and in two they do not match.  Hence the two events you ask about are each of probability $0.5$, i.e. equally likely.
A: Throwing two coins, assuming one gives head with probability 0.5 + x, the other with probability 0.5 + y: The chance for two different coins is
$(0.5 + x)(0.5 - y) + (0.5 - x)(0.5 + y)$ = 
$(1/4 - y/2 + x/2 - xy) + (1/4 + y/2 - x/2 - xy)$ = 
$(1/2 - 2xy)$
So if at least one coin is a fair coin then matching and non-matching coins are equally likely. 
If both coins prefer head or both coins prefer tails, matching coins are more likely. 
If both coins are biased in different directions, non-matching coins are more likely. 
A: You got 1/2 of chances of getting a head on the first flip and 1/2 of getting a tail.
Then on the second flip you got the same probability, so 1/2 and 1/2.
If you compute the matrix of the combinations that you can get:
(a) Head 1st flip, Head 2nd flip
(b) Head 1st flip, Tail 2nd flip
(c) Tail 1st flip, Head 2nd flip
(d) Tail 1st flip, Tail 2nd flip
All of these combinations have a probability of 1/4 to appear (1/2 for the first flip * 1/2 for the second flip); so the probability of two coins to match is 2/4 (i.e.: 1/2) because 1/2 + 1/2 is 2/4 :)
The same applies for the probability of two coins to be different
A: Assuming each coin is a fair coin (i.e. the one in which Heads and Tails appear with $\frac12$ probability each, all outcomes (${HH, HT, TH, TT}$) are equally likely, all with equal probability $\frac14$.
However, if the coin is biased, i.e. coin has probability $p$ of getting Heads and probability $1-p$ of getting Tails, then $P(HH) = p^2, P(HT) = P(TH) = p(1-p), P(TT) = (1-p)^2$, where $0 \le p \le 1$.
You can verify that these probabilities add up to $1$.
A: *

*H = head

*T = tail


You can just count them:


*

*50% (HH or TT)

*50% (HT or Th)



