For each of the following probabilities, write “dependent” if the outcome of the second event depends on the outcome of the first event and “independent” if it does not.

1. P(spinning a $3$ on a spinner after having just spun a $2$)

   Hint (a):

   Does the outcome of your spin affect what you spin the next time?

   Answer (a):

   Independent

2. P(drawing a red $6$ from a deck of cards after the $3$ of spades was just drawn and not returned to the deck)

   Hint (b):

   Has the number of sixes changed? Has the total number of cards changed?

   Answer (b):

   Dependent, since there are fewer cards in the deck after the initial draw.

3. P(drawing a face card from a deck of cards after a jack was just drawn and replaced and the deck shuffled again)

   Hint (c):

   Are there now fewer face cards if the jack was drawn and replaced? If not, then the probability is independent.

4. P(selecting a lemon-lime soda if the person before you reaches into a cooler full of lemon-lime sodas, removes one, and drinks it)

   Hint (d):

   If there are only lemon-lime sodas to choose from, what are your chances of selecting a lemon-lime soda?
   Does this change if there are fewer sodas in the cooler?