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Boxes with Yellow and Green Balls
Three boxes contain yellow and green balls
- Box 1 contains 2 yellow balls.
- Box 2 contains 2 green balls.
- Box 3 contains 1 yellow ball and 1 green ball.
One box is selected at random, and one ball is pulled out of that box.
- The ball that is pulled out of the chosen box is yellow. What is the probability that the other ball in that same box is also yellow?
- Let \(A\) be the event that Box 3 is chosen. Let \(B\) be the event that a yellow ball is pulled out of the chosen box. Are \(A\) and \(B\) independent?
- The ball that is pulled out of the chosen box is yellow. Without replacement, a second ball is chosen at random from one of the three boxes. (Each box has a 1/3 chance of being selected.) What is the probability that the second ball chosen is also yellow?
A strange deck of cards
In a non-standard deck of cards there are
- 20 blue cards (numbered 1 through 20),
- 20 green cards (numbered 1 through 20), and
20 red cards (numbered 1 through 20)
Four cards are dealt without replacement from this deck.
- What is the probability that exactly two of the four cards dealt are blue?
- Given that at least one of the first two cards dealt is blue, what is the probability that exactly three of the four cards dealt are blue?
- What is the probability that at least two of the four cards dealt have the same numeric value (1 through 20)?
Which deck is rigged ?
Two decks of cards are sitting on a table. One deck is a standard deck of 52 cards. The other deck (called the rigged deck) also has 52 cards but has had 4 of the 13 Harts replaced by Diamonds. (Recall that a standard deck has 4 suits: Diamonds, Harts, Spades, and Clubs. normal there are 13 of each suit.)
- What is the probability one chooses 4 cards from the rigged deck and gets exactly 2 diamonds and no hearts?
- What is the probability one chooses 4 cards from the standard deck and gets exactly 2 diamonds and no hearts?
- You randomly chose one of the decks and draw 4 cards. You obtain exactly 2 diamonds and no hearts.
- What is the probability you chose the cards from the rigged deck?
- What is the probability you chose the cards from the standard deck?
- If you had to guess which deck was used, which would you guess? The standard or the rigged ?
