Calculating Probability of Dependent Events

PROBABILITY DEPENDENT AND INDEPENDENT EVENTS

• Raji and Kara must each choose a topic from a list of topics to research for their class. If Raji’s choice has no effect on Kara’s choice and vice versa, the events are independent. For independent events, the occurrence of one event has no effect on the probability that a second event will occur.

• If once Raji chooses a topic, Kara must choose from the remaining topics, then the events are dependent. For dependent events, the occurrence of one event does have an effect on the probability that a second event will occur.

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Decide whether the set of events are dependent or independent. Explain your answer.

Kathy draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number cube.

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Yuki chooses a book from the shelf to read, and then Janette chooses a book from the books that remain.

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Joann flips a coin and gets a head. Then she

rolls a 6 on a number cube.

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Annabelle chooses a blue marble from a set

of three, each of different colors, and

then Louise chooses a second marble from the remaining two marbles.

To find the probability that two independent events will happen, multiply the probabilities of the two events.

Find the probability of choosing a green marble at random from a bag containing 5 green and 10 white marbles and then flipping a coin and getting tails.

• P(GREEN) 5/15 OR 1/3

• P(TAILS) 1-2

• P(GREEN AND TAILS) 1/3 * 1/2 = 1/6

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Find the probability of choosing a red marble at random from a bag containing 5 red and 5 white marbles and then flipping a coin and getting heads.

To find the probability of two dependent events, you must determine the effect that the first event has on the probability of the second event.

A reading list contains 5 historical books and 3 science-fiction books. What is the probability that Juan will randomly choose a historical book for his first report and a science-fiction book for his second?

DEPENDENT EVENTS

• P(HISTORICAL BOOK) 5/8

• P (SCIENCE-FICTION) 3/7

• P (HISTORICAL THEN SCI-FI) 5/8*3/7=15/56

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Alice was dealt a hand of cards consisting of 4 black and 3 red cards. Without seeing the cards, what is the probability that the first card will be black and the second card will be red?

Multiple Choice

Decide whether each event is independent or dependent.

Mary chooses a game piece from a board game, and then Jason chooses a game piece from three remaining pieces.

• DEPENDENT

• INDEPENDENT

Multiple Choice

Decide whether each event is independent or dependent.

Regina flips tails on a coin and rolls 5 on a number cube.

• DEPENDENT

• INDEPENDENT

Multiple Choice

Find the probability of spinning an evenly divided spinner numbered 1–8 and getting a PRIME number on one spin and getting an ODD number on a second spin.

• 1/2

• 4/8

• 1/4

• 3/16

Multiple Choice

Sarah picks 2 hats at random from 5 bill caps and 3 beanies. What is the probability that both are bill caps?

• 5/8

• 3/8

• 15/64

• 5/14

Multiple Choice

What is the probability that Lupe will choose 2 apples from a bin of 10 apples, 8 bananas, and 7 oranges?

• 2/25

• 3/20

• 11/25

• 18/25

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Joann flips a coin and gets a head. Then she

rolls a 6 on a number cube.