## 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:

The gambler is permitted to discard two cards, and be dealt two new cards from the dealer. Should the gambler
• Discard the 4 and the Queen in hopes for a full house? (a full house requires that the gambler is dealt either a 3 and a Queen or two Queens)
• Or should she discard a 3 and a Queen, in hopes for a straight? (a straight requires that she be dealt a 2 and a 6 or a 5 and a 6)

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:

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?

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 5ora 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).
• Select one card from an ordinary deck. E1 = {selecting a King} and E2 = {selecting a face card} [Solution]

• Select three cards from an ordinary deck. E1 = {selecting 3 black cards} and E2 = {selecting 1 red card and 2 black cards} [Solution]

• Select two cards from an ordinary deck. E1 = {selecting only one heart} and E2 = {selecting only one 9} [Solution]

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

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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