Independent and Dependent Events

1. SECTION 4-5
Independent and Dependent Events

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

3. VOCABULARY
1. Independent:
2. Dependent:

4. VOCABULARY
1. Independent: When the result of the second event is not
affected by the result of the first event
2. Dependent:

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

20. PROBLEM SET

21. PROBLEM SET
p. 170 #1-25
“Most people would rather be certain they’re miserable
than risk being happy.” - Robert Anthony