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ALGEBRA 2

Name _____________________________Per______

Probability of an event is a number between _________ and_________ that indicates the likelihood the event will occur. Theoretical probability is defined as P ( A) = _______________________________________. Experimental probability is defined as P ( A) = _______________________________________. 1. You roll a six-sided die 25 times. A 4 is rolled 6 times.

Express your answer as a fraction.

a. What is the theoretical probability of rolling a 4?

b. What is the experimental probability of rolling a 4?

2. You have an equally likely chance of spinning any value on the the spinner. Find the probability of spinning the given event. Express your answer as a fraction. a. A prime number is chosen.

b. A multiple of 15 is chosen.

12 1 11 10

2 3

9

4 8

5 7

c. A multiple of 4 is chosen.

d. A single-digit number is chosen.

e. A factor of 36 is chosen

f. An odd number or a perfect square

6

3. A game at the state fair has a circular target with a radius of 12 centimeters on a square board

measuring 30 centimeters a side, as shown. Players win if they are able to throw a dart and hit the circular area only. a. What is the probability that a dart will hit the circular region?

b. What is the probability that a dart will hit the square region that is outside the circle?

c. In order for a player to win a prize, that player must hit the circular region with 3 consecutive darts (darts removed after each toss).

What is the probability of a player winning a prize?

Two events are independent if the occurrence of one has ___________ effect on the occurrence of the other. Problems would say, “Find P(A and B) with replacement”. If A and B are independent events, then the probability that both A and B occur is defined as

P ( A and B ) = _____________________________________

Two events are dependent if the occurrence of one __________________________the occurrence of the other. Problems would say, “Find P(A and B) without replacement”. If A and B are dependent events, then the probability that both A and B occur is defined as P ( A and B ) = __________________________________

4. State whether the events are independent or dependent. a. You select a marble and then choose a second marble without replacing the first marble.

c. Your teacher chooses one student to lead a group and then chooses another student to lead a different group.

b. You roll a number cube and spin a spinner.

d. You reach into your sock drawer, pull out a sock without looking, and put it on. Then you reach back into the drawer, pull out another sock without looking, and put that one on.

5. Find the probability of drawing the given cards from a standard 52-card deck (a) with replacement and (b) without replacement. Express your answer to 4 significant (non zero) decimal places.

a. a face card, then an ace i.

b. a king, then another king, then a third king ii.

i.

ii.

6. A jar contains 12 green marbles, 10 blue marbles, and 8 yellow marbles. Find the probability of choosing the given marbles from the jar (a) with replacement and (b) without replacement. Express your answer to 4 significant (non zero) decimal places. a. green, then green, then blue i.

b. green, then blue, then yellow ii.

i.

ii.

7. Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting one green marble from bag A and one black marble from bag B. Express your answer to 4 significant (non zero) decimal places.

Are the two events independent or dependent?

Why?

2 events are overlapping if the events have______ or _________ common members.

2 events are disjoint if the events have___________ common members.

The formula for the probability of overlapping events is:

The formula for probability of disjoint events is:

P( A or B) = ________________________________.

P( A or B) = ________________________________.

8. An Educational Advisor estimates that there is a 90% probability that a freshman college student will take either a mathematics class or an English class, with an 80% probability that the student will take a mathematics class and a 75% probability that the student will take an English class. What is the probability that a freshman college student will take both a mathematics class and an English class? Write down the formula that you use. SHOW ALL WORK.

9. You are performing an experiment to determine how well pineapple plants grow in different soils. Out of the 40 pineapple plants, 16 are planted in sandy soil, 18 are planted in potting soil, and 7 are planted in a mixture of sandy soil and potting soil. What is the probability that a pineapple plant in the experiment is planted in sandy soil or potting soil? Write down the formula that you use. SHOW ALL WORK.

10. You roll a die. Find P(A or B). Write down the formula that you use. SHOW ALL WORK. a. Event A: Roll a 2.

Event B: Roll an odd number.

b. Event A: Roll an even number.

Event B: Roll a number greater than 3.

The set of all outcomes in the sample space that are not in E is called the ____________________________________ of event E. It is defined as P(not E) = _____________________________________. 11. You randomly draw a marble out of a bag containing 4 green marbles, 6 blue marbles, 8 yellow marbles, and 2 red marbles. Find the probability of drawing a marble that is not yellow. (Use complements to find the answer.) Express your answer as a fraction.

12. A card is randomly drawn from a standard 52-card deck. Find the probability of the given event using COMPLEMENTS. Express your answer as a fraction and as a decimal rounded to three places.

a. not an ace

b. not a diamond

13. In a survey, 8 people exercise regularly and 22 people do not. Of those who exercise regularly, 1 person felt tired. Of those that did not exercise regularly, 6 person felt tired. 2-WAY FREQUENCY TABLE a. Organize these results in a two-way frequency table. b. Then find and interpret the marginal frequencies. Total

Total

c. Now make a two-way relative frequency table that shows the joint and marginal relative frequencies. Use this table to answer the questions.

2-WAY RELATIVE FREQUENCY TABLE

d. What is the probability that a randomly chosen person surveyed exercise regularly and felt tired? Total

e. What is the probability that a randomly chosen person surveyed did not exercise regularly and did not feel tired? Total

You may answer these questions using either of the above tables. f. The questions below represent ___________________________ probabilities. These are a bit more difficult than problems d and e. g. What is the probability that a randomly chosen person surveyed did not feel tired, given that he/she exercised regularly?

h. What is the probability that a randomly chosen person surveyed did not exercise, given that he/she felt tired?