SECTION 4-5Independent and Dependent Events

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

VOCABULARY

1. Independent:

2. Dependent:

VOCABULARY

1. Independent: When the result of the second event is not affected by the result of the first event

2. Dependent:

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

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.

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)

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)

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

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

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

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%

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?

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)

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)

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

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

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

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%

PROBLEM SET

PROBLEM SET

p. 170 #1-25

“Most people would rather be certain they’re miserable than risk being happy.” - Robert Anthony