Independent and Dependent Events

1. SECTION 4-5
Independent and Dependent Events
Friday, December 17, 2010

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
Friday, December 17, 2010

3. VOCABULARY
1. Independent:
2. Dependent:
Friday, December 17, 2010

4. VOCABULARY
1. Independent: When the result of the second event is not
affected by the result of the first event
2. Dependent:
Friday, December 17, 2010

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
Friday, December 17, 2010

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.
Friday, December 17, 2010

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)
Friday, December 17, 2010

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)iP (Black)
Friday, December 17, 2010

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)iP (Black)
26 26
= i
52 52
Friday, December 17, 2010

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)iP (Black)
26 26 676
= i =
52 52 2704
Friday, December 17, 2010

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)iP (Black)
26 26 676 1
= i = =
52 52 2704 4
Friday, December 17, 2010

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)iP (Black)
26 26 676 1
= i = = = 25%
52 52 2704 4
Friday, December 17, 2010

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?
Friday, December 17, 2010

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)
Friday, December 17, 2010

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)iP (Black)
Friday, December 17, 2010

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)iP (Black)
26 25
= i
52 51
Friday, December 17, 2010

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)iP (Black)
26 25 650
= i =
52 51 2652
Friday, December 17, 2010

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)iP (Black)
26 25 650 25
= i = =
52 51 2652 102
Friday, December 17, 2010

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)iP (Black)
26 25 650 25
= i = = ≈ 24.5%
52 51 2652 102
Friday, December 17, 2010

20. PROBLEM SET
Friday, December 17, 2010

21. PROBLEM SET
p. 170 #1-25
“Most people would rather be certain they’re miserable
than risk being happy.” - Robert Anthony
Friday, December 17, 2010