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Unit 8, Lesson 11

Probabilities in Games

Geometry

Practice

Problem 1

ForLesson 10: Using Probability to Determine Whether Events Are Independent

The two-way table shows the number of eggs laid by 10 Rhode Island red chickens and 10 leghorn chickens in July and August.

A chicken is selected at random. For each question, Event A is “egg laid by a Rhode Island red chicken” and Event B is “egg laid in July.” Use the data to estimate the probabilities.

	eggs laid in July	eggs laid in August
Rhode Island red chicken	247	252
leghorn chicken	239	241

\(P(\text{A})\)
\(P(\text{B})\)
\(P(\text{A and B})\)
\(P(\text{A | B})\)
Use \(P(\text{A | B}) = P(\text{A})\) and \(P(\text{A and B}) = P(\text{A}) \boldcdot P(\text{B})\) to determine if the two events are dependent or independent. Show or explain your reasoning.

Problem 2

ForLesson 9: Using Tables for Conditional Probability

The two-way table summarizes whether or not a softball team had practice when it was raining and when it was not raining at the start of the day.

	softball practice	no softball practice
raining	4	1
not raining	12	3

When it was raining at the start of the day, what is the probability that softball practice was held?
When it was not raining at the start of the day, what is the probability that softball practice was held?
Are the events of “holding softball practice” and “raining at the start of the day” dependent or independent events? Explain your reasoning.

Problem 4

ForLesson 6: The Addition Rule

A total of 40 elementary, middle, and high school students participate in a fun run as a fundraiser. They are surveyed after the fun run to find out how many of them completed the fun run without walking. The results of the survey are shown in the table.

	elementary	middle	high
walked during the fun run	8	2	1
did not walk during the fun run	4	14	11

Mai, wants to know the probability that one of the participants in the fun run selected at random is an elementary school student or did not walk during the fun run. To figure this out, she adds the three values in the second row of the table (4, 14, and 11) to the two values listed under the heading “elementary school” (8 and 4). She then divides that answer by 40 and obtains a probability of \(\frac{41}{40}\). Mai realizes that \(\frac{41}{40}\) is greater than 1 and determines that she must have made a mistake.

What is Mai's mistake? Explain your reasoning.
How does the addition rule account for this kind of mistake?

Problem 5

ForLesson 5: Combining Events

Two classes of middle school students who are going on a field trip were asked if they wanted to go to a science museum or an art museum. Each student selects one museum option. The table summarizes the museum preference of each student in the class.

	science museum	art museum
class A	14	12
class B	11	14

What is the probability that a student in class B selected at random prefers to go to the art museum?

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