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Main Idea and VocabularyExample 1:Independent EventsKey Concept: Probability of Independent EventsExample 2:Real-World ExampleKey Concept: Probability of Dependent EventsExample 3:Dependent EventsExample 4: Disjoint EventsKey Concept: Probability of Disjoint Events

• compound event• independent events• dependent events• disjoint events

• Find the probability of independent and dependent events.

Independent Events

The spinner to the right is spun and a number cube is tossed. Find the probability of spinning a C and rolling a number less than 5.

List the sample space.

A, 1 A, 2 A, 3 A, 4 A, 5 A, 6B, 1 B, 2 B, 3 B, 4 B, 5 B, 6C, 1 C, 2 C, 3 C, 4 C, 5 C, 6

Independent Events

P

P

A coin is tossed and a number cube is rolled. Find the probability of tossing heads and rolling an even number.

A.

B.

C.

D.

LUNCH For lunch, Jessica may choose a turkey sandwich, a tuna sandwich, a salad, or a soup. For a drink, she can choose juice, milk, or water. If she chooses a lunch and a drink at random, what is the probability that she chooses a sandwich and juice?

Answer: The probability that she chooses a sandwich

and juice is

CLOTHES Zachary has a blue, a red, a gray, and a white sweatshirt. He also has blue, red, and gray sweatpants. If Zachary randomly pulls a sweatshirt and a pair of sweatpants from his drawer, what is the probability that they will both be blue?

A.

B.

C.

D.

SOCKS There are 4 black, 6 white, and 2 blue socks in a drawer. José randomly selects two socks without replacing the first sock. What is the probability that he selects two white socks?

Since the first sock is not replaced, the first event affects the second event. These are dependent events.

Dependent Events

number of white sockstotal number of socks

number of white socks after one is removedtotal number of socks after one is removed

Answer: So, the probability of selecting two white socks

is or about 22.7%.

2

1

Dependent Events

GAMES Janet has a card game that uses a deck of 48 cards—16 red, 16 blue, and 16 green. If she randomly selects two cards without replacing the first, what is the probability that both are green?

A.

B.

C.

D.

MONTHS A month of the year is randomly selected. What is the probability of the month ending in the letter Y or the letter R?

Disjoint Events

These are disjoint events since it is impossible to have a month ending in both the letter Y and the letter R.

There are 8 favorable outcomes: January, February, May, July, September, October, November, or December.There are 12 possible outcomes.

Answer: So, the probability of a month ending in the

letter Y or R is .

MARBLES There are 12 yellow, 3 black, 5 red, and 8 blue marbles in a bag. Joseph randomly selects one marble from the bag. What is the probability that the marble selected will be black or red?

A.

B.

C.

D.