SOLUTION: In a game room, there are three decks of cards: Deck 1 contains 5 red cards and 3 black cards, Deck 2 contains 3 red cards and 1 black card, and Deck 3 contains 4 red cards and 2

Question 1205003: In a game room, there are three decks of cards: Deck 1 contains 5 red cards and 3 black cards, Deck 2
contains 3 red cards and 1 black card, and Deck 3 contains 4 red cards and 2 black cards. If a deck of
cards is selected at random, and then a card is drawn from the chosen deck, find the probability that
the drawn card will be red.
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
In a game room, there are three decks of cards: Deck 1 contains 5 red cards and
3 black cards, Deck 2 contains 3 red cards and 1 black card, and Deck 3 contains
4 red cards and 2 black cards. If a deck of cards is selected at random, and
then a card is drawn from the chosen deck, find the probability that the drawn
card will be red.

Let's suppose you play this games many times.

1/3 of those times you will select Deck 1, and 5/8ths of those times when you
select Deck 1, you'll draw a red card.  So that's what's happens (1/3)(5/8) =
5/24ths of ALL the many times you play.

1/3 of those times you will select Deck 2, and 3/4ths of those times when you
select Deck 2, you'll draw a red card.  So that's what's happens (1/3)(3/4) =
5/24ths of ALL the many times you play.

1/3 of those times you will select Deck 3, and 4/6ths or 2/3rds of those times
when you select Deck 3, you'll draw a red card.  So that's what's happens 
(1/3)(2/3) = 2/9ths of ALL the many times you play.

So 5/24ths + 1/4th + 2/9ths = 49/72nds of ALL those times you'll draw a red card.

Answer 49/72.

Edwin

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