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Now let me up the ante by flipping this coin twice.
Once again, I'm drawing a coin from this bag,
and I pick one at 50% chance.
I don't know which one I have picked.
It might be fair or loaded.
And in flipping it twice,
I get first heads,
and then tails.
What's the probability that if I do the following,
I draw a coin at random with the probabilities shown,
and then I flip it twice, that same coin.
I just draw it once and then flip it twice.
What's the probability of seeing heads first
and then tails?
Again, you might derive this using truth tables.