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Probability

Practice Problems



If you need some more help, you may want to review the Probability section again.

Problems With Solutions

1. Aaron selects a card from a standard deck. What is the probability that it is...
  1. a face card?
  2. less than a 4 or a heart?
  3. an ace and a face card?


2. Julia picks 3 cards from a deck of 52.
  1. What is the probability that all 3 cards are diamonds?
  2. What is the proability that all 3 cards are 7's?


3. You are dealt 4 clubs from an ordinary deck of 52. What is the probability that your next card is a club? If you are dealt two cards instead of one, what are your chances that exactly one of them is a club?



(The following problem involves the game poker. See the Poker FAQ to learn more)
4. A gambler is playing a game of poker has the following hand:

3 of Spades 4 of Hearts 5 of Diamonds 3 of Hearts Queen of Spades


The gambler is permitted to discard two cards, and be dealt two new cards from the dealer. Should the gambler


If the gambler will win more money from a full house than a straight, would you reccomend that she attempt to get a full house?



5. The following cards are laid out on a table:
10 of Hearts 5 of Hearts 7 of Hearts 2 of Hearts 9 of Hearts 6 of Hearts


If you randomly select 2 cards, what is the probability that you add the values of the cards selected and get an even number? that the cards you select are both prime?



6. A standard deck of cards is divided into two piles: the red cards (hearts and diamonds) and the black cards (clubs and spades). A cube numbered 1-6 is rolled; if an even number appears, a card is selected from the red pile. If an odd number is rolled, a card is drawn from the black pile.

  1. what is the probability that a red card is selected?
  2. if a two is rolled, what is the probability that of selecting a diamond?
  3. given that a 5 of spades is selected, what is the probability that a 4 was rolled?
  4. what is the probabilty that a face card is drawn given that a 3 was rolled?



On Your Own



1. What is the probability that a card randomly selected it is...
  1. a black Queen or a red King? [Solution]
  2. a number divisible by 5ora spade? [Solution]
  3. either a red card or a black card? [Solution]

Do the probabilities differ if there are 2 decks to pick from? [Solution]



2. Faith picks 3 cards from a deck of 52.
  1. What is the probability that all 3 cards are the same color? [Solution]
  2. What is the proability that exactly one card is a 9? [Solution]
  3. What is the proability Faith has at least 2 hearts? [Solution]


3. In each scenario below, determine if the two events E1 and E2 are mutually exclusive, and then compute P(E1 or E2).

4. A jug contains 4 red balls, 3 blue balls, and 2 green balls. Two balls are drawn randomly.

This is a badly drawn jug

Find:

  1. P(first ball is blue) [Solution]
  2. P( 2nd ball blue | 1st ball green ) [Solution]
  3. P( 2nd not green | 1st ball not green ) [Solution]
  4. P( 2nd ball blue | 1st ball not blue ) [Solution]





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