GSE Math 7-8 Unit 3 – Probability Study Guide

Name ______

MGSE7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

1.  If Joe had an 80% chance of a successful outcome on his science project, what is the probability of this project being successful?

a) certain b) equally likely and unlikely (even chance) c) likely d) unlikely

2.  If Maria’s chances of winning the game was unlikely, which answer BEST represents her probability?

a) 0 b) 0.5 c) 1.0 d) 0.25

3.  If the probability of P(rain) is 65%, what is the complement of this event expressed as a fraction, decimal, & percent?

MGSE7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency. Predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

4.  There are 15 girls and 10 boys in Ms. Garcia’s class. Each day she randomly asks one student to take attendance. In 125 school days, which is the best prediction for the number of times that the student will be a girl?

a) 75 b) 50 c) 100 d) 150

5.  John will roll a fair number cube a total of 72 times. What is a good prediction for the number of times that the number cube will land on a 5?

a) 36 b) 48 c) 12 d) 360

MGSE7.SP.7 Develop a probability model and use it to find probabilities of events. Compare experimental and theoretical probabilities of events. If the probabilities are not close, explain possible sources of the discrepancy.

For problems 6 – 7, you have thirty-six tiles numbered 1 through 36. Eight of the tiles are red, twelve of the tiles are purple, six of the tiles are green, and ten of the tiles blue. Find the theoretical probability of the following event:

6.  P(purple)?

7.  P(even or blue)?

For problems 8 – 9. Suppose you roll a 6-sided fair number cube. Find each probability as a fraction, decimal and a percent.

8.  P(NOT 6)?

9.  P(5 or higher)?

10.  Using the tables above, for which possible outcome did the results of the class experiment match the theoretical probability?

a) 3 heads b) 2 heads and 1 tail c) 1 head and 2 tails d) 3 tails

MGSE7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

11.  What is the probability of the arrow landing on a composite number in single spin?

12.  Drake and three friends have a tradition of meeting every week for lunch. Each week they use a spinner to determine who gets to choose the next place.

Drake has gotten to choose three times in a row.

(a)  What’s the probability of such an occurrence?

(b)  What’s the probability that Drake gets to choose the fourth week as well?

(c)  What’s the probability that Wale or Taylor Swift gets to choose the following week?

MGSE7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open‐end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

13.  A sports store sells water bottles in different colors. The table shows the colors of the last 200 water bottles sold. The manager plans to order 1800 new water bottles. How many red water bottles should the manager order? green water bottles? clear water bottles?

MGSE7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

John drops 18 marbles into a jar. There are 8 black marbles, 7 red marbles, and 3 silver marbles. / If 2 marbles are chosen with replacement, what is the probability of choosing a black marble and a silver marble?
P(black and silver) =
=
=

14.  A and B are independent events. If P(A) = 0.3 and P(B) = 0.2, what is the value of P(A and B)?

Jill has 6 blue Orbeez, 3 green Orbeez, and 1 white Orbeez in a bag.

15.  Jill draws an Orbeez without looking from the bag. What is the probability that the Orbeez is either green or white?

16.  A coin is tossed one time, and a 4-color spinner, shown below, is spun once. What is the probability that the coin will show tails and the spinner will not point to green?

17.  There are 18 members in the Gotta Dance Group on America’s Best Dance Crew. Eight of the members are girls, 10 are boys and of those, 9 have siblings who are in elementary school. The producer of the show wants to choose one representative at random from the Gotta Dance Group to serve as a spokesperson for the next season of the show. What is P(girl or sibling in elementary school)?

MGSE7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

For problems 18 -19, Josh works at Walker’s Deli making sandwiches. Each sandwich has 1 type of cheese and 1 type of meat on bread. The deli has white, wheat, and rye bread available. The meat choices are turkey and ham, and the cheese choices are American and Swiss. Use the tree diagram to answer the question below.


18.  How many possible sandwiches can Josh make at the deli?

19.  How many of the sandwich combinations will contain ham?

20.  Suppose you have two pairs of pants (blue and black), four shirts (pink, white, blue, and green), and two pairs of shoes (brown and orange). Find the sample space by drawing a tree diagram. What is the probability or wearing a blue pair of pants with a pink shirt and brown shoes?

21.  A fair coin is tossed and a marble is selected from a bag. No two marbles in the bag are the same color. If there are a total of 36 outcomes in the sample space, how many marbles are in the bag?

22.  A car is sold in three models: EV, SV, and LV. It comes in six colors: black, white, red, silver, lime, or blue. How many different ways are there to choose one model and one color of that car?

23.  A new cell phone has just been released. There are three different TALK plans and two TEXT plans to choose from. If the company would like to have 36 different combinations of plans, how many different DATA plans should they offer?

24.  During an experiment, the two spinners below will be spun at the same time. Represent the sample space.

MGSE7.SP.8c Explain ways to set up a simulation and use the simulation to generate frequencies for compound events. For example, if 40% of donors have type A blood, create a simulation to predict the probability that it will take at least 4 donors to find one with type A blood?

Use the table of random numbers to simulate the situation for numbers 25-26.

25.  Let the numbers 1 - 5 represent people who order Cobb salad. Checking in rows, how many people would you have to survey before you find 5 people who ordered Cobb salad?

26.  What is the probability represented in question number 25?

27.  Of the 100 customers represented in the random number table, what is the probability to the nearest percent that the customer will order Cobb salad?