There are two coins in a bag:
- Coin A: has a face on both sides.
- Coin B: it is normal (heads and tails).
You pull out a coin at random, flip it and it comes up heads.
What is the probability that the other side of that same coin is also heads?
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The two-sided coin
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- When conditioning on “heads,” the equiprobable cases are these three observations:
- In 2 out of 3 cases you are in the double-sided coin.
- Final section: normal coin, heads side. In 2 out of 3 cases you are in the double-sided coin. Reusable idea: in conditional probability you have to reconstruct the sample space after the evidence. Then, when conditioning on “heads,” the equiprobable cases are these three
Solution
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Answer: $\tfrac{2}{3}$.
When conditioning on “heads,” the equiprobable cases are these three observations:
- double-sided coin, side 1,
- double-sided coin, side 2,
- normal coin, face side.
In 2 out of 3 cases you are in the double-sided coin.
Reusable idea: in conditional probability you have to reconstruct the sample space after the evidence.
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