There is a bag that contains 20 silver coins and 10 gold coins. You are the sixth person in line to randomly draw and keep a coin from the bag.
a) What is the probability that you draw a gold coin?
b) If you draw a gold coin, what is the probability that the five people ahead of you all drew silver coins?
How do I account for the reduction in coins from each draw when it may be a gold or silver coin. Normally I could just reduce the probability of a collections of coins by reducing one, but since I am the sixth person I line how do I know what the number of gold and silver coins will be?
The probability the first person draws a gold is (1/3) and that they draw a silver is (2/3), but how does this influence the draw of the second person. Depending on what the first person drew (which is unknown) the second person will have different probabilities for gold and silver coins, but how do I account for that and continue that chain to the sixth person (me)?