SWBAT: Apply the general multiplication rule to solve probability questions.
Lesson 5-3
Do Now:
A town has one high school, which busses students from urban, suburban, and rural ​
communities. Which of the following samples is recommended in studying attitudes toward ​
tracking of students in honors, regular and below-grade level classes? ​
(A) Convenience Sample ​
(B) Simple random sample (SRS) ​
(C ) Stratified sample ​
(D) Systematic sample ​
(E) Voluntary response sample ​
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Tree Diagrams and the General Multiplication Rule ​
The two-way table showing the gender and handedness of the students in a class is shown ​
below. ​
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Suppose we choose two students at random. ​
(a) Draw a tree diagram that shows the sample space for this chance process. ​
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(b) Find the probability that both students are left-handed. ​
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SWBAT: Apply the general multiplication rule to solve probability questions.
Lesson 5-3
General Multiplication Rule ​
P(a ​∩​ B) = P(a) · P(B | a)
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Example:
The Pew Internet and American Life Project finds that 93% of teenagers (ages 12 to 17) use the ​
Internet, and that 55% of online teens have posted a profile on a social-networking site. ​
(a) Draw a tree diagram that shows the sample space for this chance process. ​
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(b) What percent of teens are online and have posted a profile? ​
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SWBAT: Apply the general multiplication rule to solve probability questions.
Lesson 5-3
You Try! ​
According to Forrest Gump, “Life is like a box of chocolates. You never know what you’re gonna ​
get.” Suppose a candy maker offers a special “Gump box” with 20 chocolate candies that look ​
the same. In fact, 14 of the candies have soft centers and 6 have hard centers. C hoose 2 of the ​
candies from a Gump box at random. ​
(a) Draw a tree diagram that shows the sample space of this chance process. ​
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(b) Find the probability that one of the chocolates has a soft center and the other one doesn’t. ​
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SWBAT: Apply the general multiplication rule to solve probability questions.
Lesson 5-3
LESSON PRACTICE
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1. In a recent month, 88% of automobile drivers filled their vehicles with regular gasoline, 2% ​
purchased midgrade gas, and 10% bought premium gas. Of those who bought regular gas, 28% ​
paid with a credit card; of customers who bought midgrade and premium gas, 34% and 42%, ​
respectively, paid with a credit card. Suppose we select a customer at random. ​
(a) Draw a tree diagram to represent this situation. ​
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(b) What’s the probability that the customer paid with a credit card? ​
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2. A computer company makes desktop and laptop computers at factories in three states—​
C alifornia, Texas, and New York. The C alifornia factory produces 40% of the company’s ​
computers, the Texas factory makes 25%, and the remaining 35% are manufactured in New ​
York. Of the computers made in C alifornia, 75% are laptops. Of those made in Texas and New ​
York, 70% and 50%, respectively, are laptops. All computers are first shipped to a distribution ​
center in Missouri before being sent out to stores. Suppose we select a computer at random ​
from the distribution center. ​
(a) C onstruct a tree diagram to represent this situation. ​
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(b) Find the probability that the computer is a laptop. Show your work. ​
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SWBAT: Apply the general multiplication rule to solve probability questions.
Lesson 5-3
LESSON PRACTICE
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3. Morris’s kidneys are failing, and he is awaiting a kidney transplant. His doctor gives him this ​
information for patients in his condition: 90% survive the transplant and 10% die. The ​
transplant succeeds in 60% of those who survive, and the other 40% must return to kidney ​
dialysis. The proportions who survive five years are 70% for those with a new kidney and 50% ​
for those who return to dialysis. ​
(a) Make a tree diagram to represent this setting. ​
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(b) Find the probability that Morris will survive for five years. Show your work ​