Combining Two Probabilities
This will be the scenario for the next few questions: You have a bag of coins in which 10% of the coins are weighted. The weighted coins land on heads 80% of the time, while the regular coins land on heads 50% of the time.
You pick a coin at random and flip it. You again want to know the probability of two "events" happening:
Event 1 - Picking a weighted coin.
Event 2 - The weighted coin lands on heads.