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A box contains 5 red marbles and 10 blue marbles. You can take 3 marbles at random, without replacement. You win a dollar if all 3 marbles are the...

6. A box contains 5 red marbles and 10 blue marbles. You can take 3 marbles at random,
without replacement. You win a dollar if all 3 marbles are the same color.
1
(a) What is the probability of winning this game?
(b) Given that your friend played the game and won, what is the probability all the
marbles she got were blue?
(c) If you play the game 5 times (replacing the marbles after each round), what is
the chance you win at least twice?




7. A cabinet has 3 identical drawers. One drawer contains 2 gold coins, another drawer
has a gold coin and a silver coin, and the third drawer has 2 silver coins. You select a
drawer at random and take one of the coins, also at random.
(a) What is the chance you get a gold coin?
(b) Given that you got a gold coin, what is the chance the other coin in the drawer
you selected is also gold?


8. A die is rolled once. If it shows an odd number, you win the amount on the die (e.g.,
if the die shows 1, you get $1). If it shows an even number, you pay the amount on
the die.
(a) Find your expected net winnings in this game
(b) If you play this game 10 times, what is the chance you win something at least 3
times? How many wins would you expect?
(c) If you play this game until you win something and then stop, what is the chance
you play at least 3 times? How many plays would you expect?

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