int math 2 section 4-5 1011
DESCRIPTION
Independent and Dependent EventsTRANSCRIPT
![Page 1: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/1.jpg)
SECTION 4-5Independent and Dependent Events
![Page 2: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/2.jpg)
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
![Page 3: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/3.jpg)
VOCABULARY
1. Independent:
2. Dependent:
![Page 4: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/4.jpg)
VOCABULARY
1. Independent: When the result of the second event is not affected by the result of the first event
2. Dependent:
![Page 5: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/5.jpg)
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
![Page 6: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/6.jpg)
EXAMPLE 1Matt 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.
![Page 7: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/7.jpg)
EXAMPLE 1Matt 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)
![Page 8: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/8.jpg)
EXAMPLE 1Matt 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)gP (Black)
![Page 9: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/9.jpg)
EXAMPLE 1Matt 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)gP (Black)
=
2652
g2652
![Page 10: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/10.jpg)
EXAMPLE 1Matt 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)gP (Black)
=
2652
g2652
=676
2704
![Page 11: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/11.jpg)
EXAMPLE 1Matt 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)gP (Black)
=
2652
g2652
=676
2704 =
14
![Page 12: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/12.jpg)
EXAMPLE 1Matt 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)gP (Black)
=
2652
g2652
=676
2704 =
14
= 25%
![Page 13: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/13.jpg)
EXAMPLE 2Fuzzy 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?
![Page 14: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/14.jpg)
EXAMPLE 2Fuzzy 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)
![Page 15: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/15.jpg)
EXAMPLE 2Fuzzy 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)gP (Black)
![Page 16: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/16.jpg)
EXAMPLE 2Fuzzy 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)gP (Black)
=
2652
g2551
![Page 17: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/17.jpg)
EXAMPLE 2Fuzzy 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)gP (Black)
=
2652
g2551
=6502652
![Page 18: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/18.jpg)
EXAMPLE 2Fuzzy 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)gP (Black)
=
2652
g2551
=6502652
=25
102
![Page 19: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/19.jpg)
EXAMPLE 2Fuzzy 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)gP (Black)
=
2652
g2551
=6502652
=25
102≈ 24.5%
![Page 20: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/20.jpg)
PROBLEM SET
![Page 21: Int Math 2 Section 4-5 1011](https://reader033.vdocuments.site/reader033/viewer/2022042614/555aaa5ed8b42a405b8b4973/html5/thumbnails/21.jpg)
PROBLEM SET
p. 170 #1-25
“Most people would rather be certain they’re miserable than risk being happy.” - Robert Anthony