Dependent Events and Independent Events

Multiple Choice

INDEPENDENT or DEPENDENT?

Two marbles are drawn from a container in such a way that the first marble drawn is replaced before selecting the second marble.

• Independent

• Dependent

Multiple Select

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

• 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

INDEPENDENT or DEPENDENT?

A bag contains some red-colored and some blue-colored marbles. First a red-colored marble is drawn and then, without replacing the first marble, a blue-colored marble is drawn.

• Independent

• Dependent

Multiple Choice

INDEPENDENT or DEPENDENT?

The spinner is spun twice. It lands on red first and then blue?

• Independent

• Dependent

Multiple Choice

Determine which compound event is DEPENDENT.

• Selecting a candy bar from a bag, eating the candy bar, and selecting again

• Selecting a candy bar from a bag, deciding you don't want it, replace the candy bar and select again.

Multiple Choice

INDEPENDENT or DEPENDENT?

Two fair coins are flipped at the same time.

• Independent

• Dependent

Multiple Choice

INDEPENDENT or DEPENDENT?

Amy plays card games. She picks a card at random. Then WITHOUT putting the first card back, she picks a second card at random.

• Independent

• Dependent

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

Probability of an Independent Event

Use the formula for the probability of independent events.

P(A and B) = P(A)⋅P(B)

Example: Find the probability of spinning an odd number on a spinner numbered 1 - 5; and the probability of flipping a coin and landing on tails.

Tree Diagram

Flipping a coin and landing on heads or tails. There are three favorable outcomes in the sample space: HHT, HTH, and THH.

P(2 heads and 1 tails) =

Independent Events

• 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.

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?

Hint

Look for the words "with replacement" (independent events) or "without replacement" (dependent events) to help you determine whether events are independent or dependent.