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Let's do the truth table.
You have a pick event followed by a flip event.
We can pick coin 1 or coin 2.
There is a 0.5 chance for each of the coins.
Then we can flip and get heads or tails
for the coin we've chosen.
Now what are the probabilities?
I'd argue picking 1 at 0.5
and once I pick the fair coin, I know that the
probability of heads is, once again, 0.5
which makes it 0.25.
The same is true for the fair coin and
expecting tails,
but as we pick the unfair coin with a 0.5 chance,
we get a 0.9 chance of heads.
So 0.5 times 0.95 gives you 0.45,
whereas the unfair coin,
the probability of tails is 0.1
multiply by the probability of picking it at 0.5
gives us 0.05.
Now when they ask you, what's the probability of heads,
we'll find that 2 of those cases
indeed come up heads,
so if you add 0.25 and 0.45
and we get 0.7.
So this example is a 0.7 chance
that we might generate heads.