int2 section 4-5 1011

SECTION 4-5Independent and Dependent Events

Friday, December 17, 2010

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

VOCABULARY

1. Independent:

2. Dependent:

Friday, December 17, 2010

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

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

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.

Friday, December 17, 2010

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)

Friday, December 17, 2010

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)iP (Black)

Friday, December 17, 2010

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)iP (Black)

=

2652

i2652

Friday, December 17, 2010

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)iP (Black)

=

2652

i2652

=676

2704

Friday, December 17, 2010

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)iP (Black)

=

2652

i2652

=676

2704 =

14

Friday, December 17, 2010

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)iP (Black)

=

2652

i2652

=676

2704 =

14

= 25%

Friday, December 17, 2010

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?

Friday, December 17, 2010

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)

Friday, December 17, 2010

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)iP (Black)

Friday, December 17, 2010

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)iP (Black)

=

2652

i2551

Friday, December 17, 2010

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)iP (Black)

=

2652

i2551

=6502652

Friday, December 17, 2010

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)iP (Black)

=

2652

i2551

=6502652

=25

102

Friday, December 17, 2010

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)iP (Black)

=

2652

i2551

=6502652

=25

102≈ 24.5%

Friday, December 17, 2010

PROBLEM SET

Friday, December 17, 2010

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