What is the probability of obtaining an even number from rolling a fair six-sided dice?

There are two treasure chests, A and B. Treasure chest A contains 100 gold coins, and treasure chest B contains 50 gold coins and 50 silver coins. You open a chest at random, and draw a coin at random. If the coin is gold, what is the probability that you opened chest A?

If I flip a fair coin, and get \(\$1\) if it comes up heads, and \(\$2\) if it comes up tails, what is the expected value of the amount of money I win?

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