Practice Problem Set 2

1.Imagine I throw a fair 4-sided die once. Which of the following does not belong to the event space?

{1, 2, 3, 4}

{2}

{1, 4}

{3, 3, 3}

2.I have a 20-sided die. What is the size of the event space associated with rolling the die once? (You can use a calculator for this if needed.)

20

1,048,576

4,072

20,060,500

3.I roll a loaded 6-sided die.

Define the following marginal probabilities: P({1}) = 0, P({2}) = 1/3, P({3}) = 1/6, P({4}) = 1/6, P({5}) = 1/3, P({6}) = 0.

Let event Q = "Roll a multiple of 3." What is the probability of event Q?

5/6

1/2

1/3

1/6

4.We have a fair deck which includes all of the 52 different cards (13 cards of 4 different suits). What is the size of the event spacedefined by an experiment that draws a card from this deck?

522

252

52

it cannot be determined from the information given

5.We have two experiments. For the first experiment, we will draw a card at random from a fair deck of cards (52 cards with 13 cards of each suit).For the second experiment we will draw a card at random from a different fair deck of cards.

Let event R1be defined as "the carddrawn from the first deck has a red suit", event B1be "the card drawn from the first deck has a black suit", event F2be "the card drawn from thesecond deck is a figure (Jack, Queen, King, or Ace)" and event N2be "the card drawn from the second deck has a number between 2 and 10".

What is the probability of the complement of event B1U N2? (Hint: Draw a tree diagram)

1/13

2/13

1/4

4/13

6.

There are two chocolate boxes: Box 1 and Box 2. You randomly choose a box and then randomly draw a chocolate from the box you chose. Box 1 contains one White Raspberry fudge and two Dark Rum fudges. Box 2 contains two White Raspberry fudges and three Spiced Pumpkin fudges. Refer to the tree diagram below. 1What is the probability that you choose Box 1 and draw a White Raspberry fudge? WHITE RASPBERRY . DARK RUM lNHI'I'E RASPBERRY SPICED PUMPKIN O 1m (3. 235 O 133 (31 1x2 You will toss a coin up to three times. Refer to the tree diagram below. What is the rule of the game? Head You win. Head You lose. You lose. D You win whenever you get two Heads. C) You win only when you get two Heads in a row. C) You win only when you get two Tails in a row. C) You win whenever you get two Tails