TITLE: Tossing 2 Coins, Fair coin and a two headed coin
QUESTION [2 upvotes]: There are two coins. One is two headed coin, the other one is a fair coin. A coin is selected randomly and flipped.
a) what is the probability of selecting a fair coin?
b) what is the probability of head from the flipped coin?
c) what is the probability of selecting a fair coin and having head on the top?
So A and B are relatively simple, because A is $1/2$ and for B its $3/4$
but I am concerned with C
Shouldn't be the chance of having a fair coin $+$ head
is basically $1/4$? Correct me if I am wrong but
If I want to pick a fair coin, the probability is $0.5$, lets say we picked it, and now we are going to throw it, isn't also chance between head and tail is $0.5$?
Which effectively means that getting a head from a fair coin
the intersection between them is $0.5\times0.5$ which equals $0.25$?

REPLY [4 votes]: Let $F=$ "select a fair coin", and $H=$ "appear head on top"
$$P(F\cap H)=P(H|F)\cdot P(F)=\frac{1}2\cdot\frac{1}2=\frac{1}4$$
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