Prentice Hall Algebra 2

Chapter 11 Probability and Statistics > 11-3 Probability of Multiple Events > Practice and Problem-Solving Exercises

A and B are independent events. Find P(A and B).

P ( A ) = 1 6 , P ( B ) = 2 5 p open eh close equals , 1 sixth , comma p open b close equals , 2 fifths
P ( A ) = 9 20 , P ( B ) = 3 4 p open eh close equals , 9 twentieths . comma p open b close equals , 3 fourths

C and D are mutually exclusive events. Find P(C or D).

P ( C ) = 2 5 , P ( D ) = 3 5 p open c close equals , 2 fifths , comma p open d close equals , 3 fifths
P ( C ) = 1 2 , P ( D ) = 3 8 p open c close equals , 1 half , comma p open d close equals , 3 eighths
Events A and B are not mutually exclusive. If P ( A ) = 1 2 , P ( B ) = 1 4 , and P ( A and B ) = 1 8 , p open eh close equals , 1 half , comma p open b close equals , 1 fourth , comma , and p open eh , and b close equals , 1 eighth , comma find P(A or B).

Vocabulary Explain the difference between independent events and mutually exclusive events.
Error Analysis The weather forecast for the weekend is a 30% chance of rain on Saturday and a 70% chance of rain on Sunday. Your friend says that means there is a 100% chance of rain this weekend. What error did your friend make?
Open-Ended Describe two events that are mutually exclusive.

A Practice

See Problem 1.

Classify each pair of events as dependent or independent.

A month is selected at random; a number from 1 to 30 is selected at random.
A month is selected at random; a day of that month is selected at random.
A letter of the alphabet is selected at random; one of the remaining letters is selected at random.
The color of a car is selected at random; the type of transmission is selected at random.

See Problem 2.

Q and R are independent events. Find P(Q and R).

P ( Q ) = 1 4 , P ( R ) = 2 3 p open q close equals , 1 fourth , comma p open r close equals , 2 thirds
P ( Q ) = 12 17 , P ( R ) = 3 8 p open q close equals , 12 over 17 . comma p open r close equals , 3 eighths
P ( Q ) = 0.6 , P ( R ) = 0.9 p open q close equals 0.6 comma p open r close equals 0.9
P ( Q ) = 1 3 , P ( R ) = 6 7 p open q close equals , 1 third , comma p open r close equals , 6 sevenths
Reading Suppose you have five books in your book bag. Three are novels, one is a biography, and one is a poetry book. Today you grab one book out of your bag without looking, and return it later. Tomorrow you do the same thing. What is the probability that you grab a novel both days?

See Problem 3.

Two fair number cubes are rolled. State whether the events are mutually exclusive. Explain your reasoning.

End ofPage 691

Table of Contents