Question

Scenario 1: You and a friend take turns choosing cards at random from a deck containing 13 red cards and 13 black ones. Once you select a card, you record the color of the card and do not return the card to the orginal deck. Scenario 2: You and a friend take turns choosing cards at random from a deck containing 13 red cards and 13 black ones. Once you select a card, you record the color of the card and return the card to the orginal deck. a) Identify each scenario as independent or dependent. Explain your answer. b) Are the probabilities of selecting two red cards in each scenario the same or different? Explain your answer.

Answer 1

Note that both scenarios are similar, the only difference is that in scenario 1, the selected card is not returned to the deck and in scenario 2 the card is returned to the original deck.
Therefore, scenario 1 is dependent, since it "depends" on the selected cards before. If on the first attempt you have 13 blacks and 13 reds and you select a red one, then for the second attempt you will have 13 blacks and 12 reds, so this time you will have more chances of getting a black card. Scenario 2 is independent, because when you return the selected card to the deck you will always have 13 red and 13 black cards in each attempt, so each event will be independent of the previous one. Finally, as it was explained above the probability of selecting two red faces are different in each scenario