2. ESSENTIAL QUESTIONS
How do you find probabilities of dependent events?
How do you find the probability of independent
events?
Where you’ll see this:
Government, health, sports, games
5. VOCABULARY
1. Independent: When the result of the second event is not
affected by the result of the first event
2. Dependent: When the result of the second event is affected
by the result of the first event
6. EXAMPLE 1
Matt Mitarnowski draws a card at random from a
standard deck of cards. He identifies the card then
replaces it in the deck. Then he draws a second card.
Find the probability that both cards will be black.
7. EXAMPLE 1
Matt Mitarnowski draws a card at random from a
standard deck of cards. He identifies the card then
replaces it in the deck. Then he draws a second card.
Find the probability that both cards will be black.
P (Black, then black)
8. EXAMPLE 1
Matt Mitarnowski draws a card at random from a
standard deck of cards. He identifies the card then
replaces it in the deck. Then he draws a second card.
Find the probability that both cards will be black.
P (Black, then black) = P (Black)g (Black)
P
9. EXAMPLE 1
Matt Mitarnowski draws a card at random from a
standard deck of cards. He identifies the card then
replaces it in the deck. Then he draws a second card.
Find the probability that both cards will be black.
P (Black, then black) = P (Black)g (Black)
P
26 26
= g
52 52
10. EXAMPLE 1
Matt Mitarnowski draws a card at random from a
standard deck of cards. He identifies the card then
replaces it in the deck. Then he draws a second card.
Find the probability that both cards will be black.
P (Black, then black) = P (Black)g (Black)
P
26 26 676
= g =
52 52 2704
11. EXAMPLE 1
Matt Mitarnowski draws a card at random from a
standard deck of cards. He identifies the card then
replaces it in the deck. Then he draws a second card.
Find the probability that both cards will be black.
P (Black, then black) = P (Black)g (Black)
P
26 26 676 1
= g = =
52 52 2704 4
12. EXAMPLE 1
Matt Mitarnowski draws a card at random from a
standard deck of cards. He identifies the card then
replaces it in the deck. Then he draws a second card.
Find the probability that both cards will be black.
P (Black, then black) = P (Black)g (Black)
P
26 26 676 1
= g = = = 25%
52 52 2704 4
13. EXAMPLE 2
Fuzzy Jeff takes a deck of cards and draws a card at
random. He identifies it and does not return it to the
deck. He then draws a second card. What is the
probability that both cards are black?
14. EXAMPLE 2
Fuzzy Jeff takes a deck of cards and draws a card at
random. He identifies it and does not return it to the
deck. He then draws a second card. What is the
probability that both cards are black?
P (Black, then black)
15. EXAMPLE 2
Fuzzy Jeff takes a deck of cards and draws a card at
random. He identifies it and does not return it to the
deck. He then draws a second card. What is the
probability that both cards are black?
P (Black, then black) = P (Black)g (Black)
P
16. EXAMPLE 2
Fuzzy Jeff takes a deck of cards and draws a card at
random. He identifies it and does not return it to the
deck. He then draws a second card. What is the
probability that both cards are black?
P (Black, then black) = P (Black)g (Black)
P
26 25
= g
52 51
17. EXAMPLE 2
Fuzzy Jeff takes a deck of cards and draws a card at
random. He identifies it and does not return it to the
deck. He then draws a second card. What is the
probability that both cards are black?
P (Black, then black) = P (Black)g (Black)
P
26 25 650
= g =
52 51 2652
18. EXAMPLE 2
Fuzzy Jeff takes a deck of cards and draws a card at
random. He identifies it and does not return it to the
deck. He then draws a second card. What is the
probability that both cards are black?
P (Black, then black) = P (Black)g (Black)
P
26 25 650 25
= g = =
52 51 2652 102
19. EXAMPLE 2
Fuzzy Jeff takes a deck of cards and draws a card at
random. He identifies it and does not return it to the
deck. He then draws a second card. What is the
probability that both cards are black?
P (Black, then black) = P (Black)g (Black)
P
26 25 650 25
= g = = ≈ 24.5%
52 51 2652 102
