Chapter 18: Probability 257two aces is^4
524
521
131
131
169
≈06.%. If two cards are drawn without replacement, however,
the probability of drawing two aces is^4
523
511
131
171
221≈ 05 .%.
CHECK POINT
A card is drawn from a standard deck, recorded, and replaced in the deck. The deck is
shuff led, and a second card is drawn.- Find the probability of drawing a heart and then a queen.
- Find the probability of drawing a heart and then a heart.
- Find the probability of drawing a black card and then a red card.
Two cards are drawn at random from a standard deck, without replacing the first
card.- Find the probability of drawing a king and a queen.
- Find the probability of drawing two black cards.
Probabilities with “Or”
When you look at the probability of event A and event B happening, you multiply the probability
of A times the probability of B. Multiplying these two fractions, both less than one, gives a
smaller number. A smaller probability makes sense because it’s harder to have a success when
success means having two different things happen than if success means having only one thing
happen.
What if you want to find the probability of getting a five or a six when you roll a die? If you’re
willing to accept either number as a success, your chance of success increases—in this case,
it doubles. The probability of rolling a five or a six is the probability of rolling a five plus the
probability of rolling a six. PPP5 or 6 556 ^1
61
62
61
3.
If you draw a card at random from a standard deck, what’s the probability of drawing a queen or
a 10? The probability of drawing a queen is 524 = 131 , and the probability of drawing a 10 is also
4
52 = 1
13 , so the probability of drawing a queen or a 10 is4
524
521
131
132
13.
Here’s a question that sounds the same, but be very careful. Don’t jump in without thinking it
through. If you draw a card from a standard deck, what’s the probability of drawing an ace or