Probability: Independent and Dependent Events

Probability: Independent and Dependent Events

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Independent & Dependent Events

• Independent - One activity does NOT effect the outcome of a different activity. (REPLACE)

• Dependent - One activity DOES effect the outcome of another activity. (do NOT replace)

Independent Events

• To find the probability that two independent events will happen - MULTIPLY the probabilities of the two events.

Calculating Conditional Probabilities

Conditional Probability

Multiple Choice

You roll a number cube twice. The first time is a 3 and the second time is an even number.

• Independent

• Dependent

Multiple Choice

You randomly draw a marble from a bag of marbles. You get a red and don't put it back into the bag. You draw another marble out of the bag and get a yellow.

• Independent

• Dependent

Multiple Choice

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

• Independent

• Dependent

Multiple Choice

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

• Independent

• Dependent

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.

Fill in the Blank

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.

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?

Fill in the Blank

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 a black card 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 the three remaining pieces.

• Independent

• Dependent

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.

• $$\frac{1}{2}$$

• $$\frac{1}{4}$$

• $$\frac{5}{8}$$

• $$\frac{3}{16}$$

Multiple Choice

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

• $$\frac{5}{8}$$

• $$\frac{15}{64}$$

• $$\frac{3}{8}$$

• $$\frac{5}{14}$$

Multiple Choice

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

• $$\frac{2}{25}$$

• $$\frac{11}{25}$$

• $$\frac{3}{20}$$

• $$\frac{18}{25}$$

Fill in the Blank

Determine whether the scenario is independent or dependent.

Joann flips a coin and gets heads. Then she rolls a 6 on a number cube.