Checkpoint: Dependent Events Solutions

Marco has a standard deck of cards. Determine the probability of Marco randomly drawing the cards in the order listed without replacement. Round to the ten-thousandth place.

P(ace of spades, 3 of spades) $= \frac{1}{52} \cdot \frac{1}{51} = \frac{1}{2652} = 0.0004$

P(♠, ♠) $= \frac{13}{52} \cdot \frac{12}{51} = \frac{156}{2652} = 0.0588$

Note

Q: What phrase in this problem makes it dependent rather than independent probability?

A: Without replacement

Q: Why does it matter that the cards are not replaced after each draw?

A: Because the total number of cards changes, which changes the denominator.