Successfully reported this slideshow.
Upcoming SlideShare
×

# Int Math 2 Section 4-5 1011

392 views

Published on

Independent and Dependent Events

• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

### Int Math 2 Section 4-5 1011

1. 1. SECTION 4-5 Independent and Dependent EventsFriday, December 17, 2010
2. 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, gamesFriday, December 17, 2010
3. 3. VOCABULARY 1. Independent: 2. Dependent:Friday, December 17, 2010
4. 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. 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 eventFriday, December 17, 2010
6. 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. 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. 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. 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 52Friday, December 17, 2010
10. 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 2704Friday, December 17, 2010
11. 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 4Friday, December 17, 2010
12. 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 4Friday, December 17, 2010
13. 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. 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. 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. 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 51Friday, December 17, 2010
17. 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 2652Friday, December 17, 2010
18. 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 102Friday, December 17, 2010
19. 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 102Friday, December 17, 2010
20. 20. PROBLEM SETFriday, December 17, 2010
21. 21. PROBLEM SET p. 170 #1-25 “Most people would rather be certain they’re miserable than risk being happy.” - Robert AnthonyFriday, December 17, 2010