Sample Questions

1. Sue randomly picks a card from a standard deck of 52 playing cards. What is the probability that the card is red? What is the probability that the card is a king? Are those independent or dependent events?
2. Joe randomly picks two cards from a standard deck of 52 playing cards. What is the probability that both cards are kings?
3. Bill randomly picks a card from a standard deck of 52 playing cards. He then puts the card back into the deck and randomly picks another card. What is the probability that both his cards are kings?

Sample Response

1. P(red) = 1/2. P(king) = 1/13. P(red king) = 2/52. Since 1/2*1/13 = 1/26 and 2/52 = 1/26, the events are independent.
   Also, being red doesn't change the chance of being a king.
2. P(1st card king) = 4/52. P(2nd card king|1st card king) = 3/51.
   P(both kings) = 4/52 * 3/51 = 12/2652 = 1/221 = .0045 = 0.45%
   He's got less than 1% chance to pick 2 kings.
   Note: the probability of picking the second king depended on whether or not he picked the 1st king.
3. Since Bill is replacing the card, the probability that the second card is a king doesn't depend on whether or not the first was.
   P(1st card king) = 4/52. P(2nd card king|1st card king) = 4/52.
   P(both kings) = 4/52 * 4/52 = 16/2704 = 1/169 = .0059 = 0.59%
   He's got less than 1% chance to pick 2 kings. Yet it's a better chance than if he hadn't replaced the first pick.