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