Probability of Compound Events

Objectives:

1) Find probability of two independent/dependent events

2) Find probability of two mutually exclusive/inclusive events

Definitions

Independent Event

·two or more events in which the outcome of one event does not affect the outcome of another event

Example: the weather on Saturday does not affect the weather on Sunday

Compound Event

·two or more single events Example: rain on Saturday and Sunday

Simple Event

·a single event Example: rain on Saturday

Dependent Event

·two or more events in which the outcome of one event does affect the outcome of another event

Importance of probability

Probabilities_of_Risk.asf

Probability of Independent Events

If two events are independent, thenP(A and B) = P(A) P(B)

Example:

1) If there is a 40% chance of rain on Saturday and an 80% chance of rain on Sunday. What is the probability that it will rain on both days?

2) Roberta is flying from Birmingham to Chicago. The first leg of the trip is from Birmingham to Houston and the 2nd leg is from Houston to Chicago. The airline reports that the flight from Birmingham to Houston has a 90% on time record and the flight from Houston to Chicago has a 50% on time record. What is the probability that both flights will be on time?

Probability of Dependent Events

If two events are dependent, then P(A and B) = P(A) P(B following A)

Example:

At the school carnival, winners in the ring-toss game are randomly given a prize from a bag that contains 4 sunglasses, 6 brushes, and 5 key chains. Three prizes are randomly drawn from the bag and not replaced. Find each probability.

a) P(sunglasses, brush, key chain)

b) P(brush, brush, key chain)

c) P(sunglasses, brush, not key chain)

Examples of Independent and Dependent Events

A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability.

a) drawing a red chip, replacing it, then drawing a green chip

b) selecting two yellow chips without replacement

c) choosing green, then blue, then red, replacing each chip after drawn

d) choosing green, then blue, then red without replacing each chip

Probability of Mutually Exclusive Events

If two events cannot occur at the same time, then P(A or B) = P(A) + P(B)

(events that cannot occur at the same time)

Probability of Mutually Inclusive Events

(events that can occur at the same time)

If two events can occur at the same time, then P(A or B) = P(A) + P(B) - P(A and B)

(the subtraction results from the overlap)

Difference between mutually exclusive and inclusive events:

Example:

A student is selected at random from a group of 12 male and 12 female students. There are 3 male students and 3 female students from each grade. Find each probability.

a) P(9th or 12th grade)

b) P(10th grade or female)

c) P(male or female)

d) P(male or not 11th grade)

Complete Study Guide and Intervention

p. 191 - 192

Attachments

Probabilities_of_Risk.asf