PART I. P robability ► Chapter 1. Probability ► Chapter 2. Random variables 1 Duy Tan University MS. Nguyễn Tấn Huy.

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Presentation transcript:

PART I. P robability ► Chapter 1. Probability ► Chapter 2. Random variables 1 Duy Tan University MS. Nguyễn Tấn Huy

1.4 Probabilities of combined events Probability of a union Conditional Probability Probability of an interse ction

Probability of a union

Example 1 : 60% of the families in a certain community own their own car, 30% own their own home, and 20% own both their own car and their own home. If a family is randomly chosen, what is the probability that this family owns a car or a house ? Probability of a union

Exercise: At a middle school, 18% of all students play football and basketball, 40% of all students play basketball and 32% of all students play football. If a student is randomly chosen, what is the probability that a student plays football or basketball? Probability of a union

1.4 Probabilities of combined events Probability of a union Conditional Probability Probability of an interse ction

Conditional Probability

Conditional Probability Example 2: At a middle school, 18% of all students play football and basketball, and 32% of all students play football. What is the probability that a student who plays football also plays basketball?

The Multiplication Rule: Probability of an interse ction

Example 3 : A school survey found that 7 out of 30 students walk to school. If three students are selected at random without replacement, what is the probability that all three walk to school? Probability of an interse ction

The Multiplication Rule: Probability of an interse ction

Example 4: A nationwide survey showed that 65% of all children in the United States dislike eating vegetables. If 4 children are chosen at random, what is the probability that all 4 dislike eating vegetables? Probability of an interse ction