13.4 Compound Probability

A. Compound Event is an event that is made up of two or more events.

B. Independent Events: If the occurrence of an event does not affect how another event occurs. P(A and B) = P(A) ● P(B)

C. Dependent Events: If the occurrence of an event does affect how another event occurs. P(A and B) = P(A) ● P(B following A)

I. Vocabulary

D. Mutually Exclusive Events: When the events cannot occur at the same time

P(A or B) = P(A) + P(B)

E. Overlapping Events: Have outcomes in common.

P(A or B) = P(A) + P(B) – P(A and B)

NOTES: When not specified, assume it is with replacement.

A. You roll a number cube. What is the probability of rolling a 3 or 4?

 

B. You roll a number cube. What is the probability of rolling a 2 or an odd number?

II. Examples

C. A bowl of fruit is on the table. It contains 4 apples, three oranges, and 6 bananas. Travis and Paul come home from school and randomly grab one fruit each. What is the probability that one grabs an orange and the other grabs a banana?

D. Sabrina tossed a die onto a black and red checkerboard. What is the probability that it will land with value greater than 4 and on a red square?

 E. You roll a number cube. What is the probability of rolling a number less than 4 or an even number?

F. In a poll of 50 students, 19 were student council members and 33 played a winter sport. Forty-eight out of 50 were student council members or played a winter sport. What is the probability that a student is a student council member and played a winter sport?

G. You roll a number cube. What is the probability of rolling a number greater than 4 or an odd number?

H. When two number cubes are tossed, there are 36 possible outcomes. Find the probability that the sum is not 5.

I. Amanda wants to pull a diamond or spade and then a club from a deck of cards.

1. What is the probability of her being successful if when she draws the first card and she replaces it back into the deck?

. Amanda wants to pull a diamond or spade and then a club from a deck of cards.

2. What is the probability of her being successful if when she draws the first card and she DOES NOT replace it back into the deck?

Amanda wants to pull a diamond or spade and then a club from a deck of cards.

3. What is the probability of her NOT being successful if when she draws the first card and she replaces it back into the deck?