From a standard deck of cards, what is the probability of choosing .....

Question

1. a red and then a club with replacement?
2. a diamond, then a heart, then a black without replacement?

Answer 1

Hey!

For starters, we know the sample space of any standard deck is 52 (52 cards in a deck). **Remember: With Replacement: Sample size always remains the same. Without Replacement - Sample size always decreases after every event (draw, pull, etc.). Always pay attention to how many events they are pulling, drawing, lining up, etc. as your sample size should decrease accordingly!

Q1: Figure out how many red cards there are in a deck in order to write your first probability! Same with all the clubs in order to get your second probability. These are independent events, so make sure to multiply these two probabilities. Sample size will be the same for both events (denominator of 52).

Q2: Take the same approach BUT remember ONLY your sample size is decreasing by one with each draw since the cards aren't being replaced! Otherwise, count all the diamonds that you can get, then all the hearts, then all the black cards. (denominators of 52, then 51, then 50).

Hope this helps!