# Using Probability to Make Decisions

## High School Math Practice

This quiz illustrates the range of difficulty expected by the following Common Core State (CCS) standards:

 Question Common Core Standard # 1 S.MD.2 + 2 S.MD.2 + 3 S.MD.3 + 4 S.MD.3 + 5 S.MD.4 + 6 S.MD.5b +
indicates a modeling standard.
+ indicates a college and career ready standard.

All questions of this quiz illustrate the difficulty of the high school S.MD standards required for all students, including the college and career ready students.

Question 1: The probabilities of the numbers of goals scored by team A during the soccer games of a competition, were estimated in the table below:

 Number of goals Probability 0 0.4 1 0.25 2 0.15 3 0.1 4 0.1 > 5 0

If X = the number of goals scored by team A during a soccer game of the competition, calculate the expected value of X.

Question 2: An automatic lottery ticket dispenser is used to sell tickets priced at \$2 each. The table below shows the likelihood that a random customer buys a certain number of tickets.

 Number of tickets Probability 1 0.4 2 0.2 3 0.15 4 0.15 5 0.1 6 0.1

If X = the number of tickets purchased by a random customer, calculate the expected value of X.

Question 3: Which of the following tables give the probability of obtaining exactly x heads in four coin throws?

 x 0 1 2 3 4 P(x) 0.0625 0.25 0.375 0.25 0.0625

 x 0 1 2 3 4 P(x) 0.1 0.2 0.4 0.2 0.1

 x 0 1 2 3 4 P(x) 0.05 0.15 0.6 0.15 0.05

 x 0 1 2 3 4 P(x) 0.08 0.26 0.3 0.26 0.08

Question 4: Suppose you take a multiple choice test with 6 questions, and each question has 4 answers. What is the probability of getting 5 correct answers if you guess randomly on all questions?

Question 5: The probabilities for the numbers of children per family of a US city were estimated in the table below:

 Number of children Probability None 0.25 1 0.15 2 0.4 3 0.15 4 0.03 5 0.02

How many children would you expect to find in 100 randomly selected families of this city?

Question 6: Three instant lottery games have the winnings and probabilities given in the tables below:

Game A:
 Prize \$0 \$1 \$2 \$10 \$100 \$500 Probability 0.7 0.19 0.1 0.0097 0.0002 0.0001

Game B:
 Prize \$0 \$1 \$10 \$50 \$500 \$5,000 Probability 0.9 0.09 0.00889 0.0009 0.0002 0.00001

Game C:
 Prize \$0 \$1 \$5 \$10 \$200 \$1,000 Probability 0.7 0.19 0.1 0.0097 0.0002 0.0001

What of the games returns more money to the lottery players?

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