4. Draw 1 card from a standard deck of 52. Let = event that a spade turns up Red = event that a red card turns up 2 = the event that a 2 turns up. Find the following

d. P( and Red)

e. Are the events and Red disjoint?

g. Are the events and 2 disjoint?

j. P( | 2 )

5. You roll a fair die three times. What is the probability that you a. Roll all 3's?

b. You roll all odd numbers?

c. You roll at least one 5?

6. Draw 3 cards from a standard deck of 52 without replacement.

d. P(the 2nd card is the only heart)

8. Random Variables Game- Pick a card from a standard 52 card deck Cost to play - $3.00 If you choose a Red, you get nothing. If you choose a , you get $3.00. If you choose a you get $5.00. If you choose the Ace of , you get an additional $20.00.

b. What does the random variable represent? X = ________________ c. Find the player's expected resulting amount after 1 play.

d. Find the standard deviation.

e. Who has the advantage, the player or the person holding the game?