Course: Math 7B (2018) Unit: 1. PROBABILITY AND GRAPHING Assignment: 4. Sample Space
312
How many ways are there to choose a card from a deck of cards (52 cards in a deck) and roll a regular 6-sided number cube? 58 52 156 312
1/8
What is the probability that you will randomly select a Shirley's name from the list below and then roll an even number on a number cube? Names: Shirley, Shane, Shawn, and Shandra 1/2 1/8 1/6 1/4
2 + 2 + 2 + 2
Which expression would you use to find the number of outcomes for flipping 4 coins? 2 + 2 + 2 + 2 2 · 2 · 2 · 2 2(4) 2 + 4
1 2 11-1 1-2 2 2-1 2-2 3 3-1 3-2 4 4-1 4-2 5 5-1 5-2 b. 50% chance of it being odd.
A. Make an organized list to represent the sample space of tossing a coin and picking a number between 1 and 5, inclusive. [Hint: Inclusive means that 1 and 5 may be picked.] B. In your list from A, which are favorable outcomes of the following event: choosing an odd number? a. Tossing the coin would be 2 because there are two sides of a coin.
A. 15 B. 7 C. 1 D. 1
Natalie has three pairs of pants (tan, black, and blue) and five shirts (white, black, blue, green, and red). Each morning, she randomly selects one pair of pants and then one shirt. The following tree diagram represents the sample space for this compound event. Outcomes may be listed using an ordered pair. For example, tan pants and a red shirt can be listed as (tan, red). A. How many total outcomes are in the sample space? B. List the favorable outcomes for Natalie selecting a pair of pants and shirt that are the same color. C. List the favorable outcomes for Natalie selecting a black shirt. D. List the favorable outcomes for Natalie selecting at least one blue article of clothing.
(1-6) (2-5) (3-4) (4-3) (5-2) (6-1)
Second Roll 1 2 3 4 5 6 1 1-1 1-2 1-3 1-4 1-5 1-6 2 2-1 2-2 2-3 2-4 2-5 2-6 1st 3 3-1 3-2 3-3 3-4 3-5 3-6 Roll 4 4-1 4-2 4-3 4-4 4-5 4-6 5 5-1 5-2 5-3 5-4 5-5 5-6 6 6-1 6-2 6-3 6-4 6-5 6-6 Select the favorable outcomes for rolling a sum of seven. (5-1) (5-2) (5-3) (5-4) (5-5) (5-6) (1-1) (2-2) (3-3) (4-4) (5-5) (6-6) (1-6) (2-5) (3-4) (4-3) (5-2) (6-1) (1-1) (1-2) (1-3) (2-1) (2-2) (3-1)
(1-1) (1-2) (1-3) (2-1) (2-2) (3-1)
Second Roll 1 2 3 4 5 6 1 1-1 1-2 1-3 1-4 1-5 1-6 2 2-1 2-2 2-3 2-4 2-5 2-6 1st 3 3-1 3-2 3-3 3-4 3-5 3-6 Roll 4 4-1 4-2 4-3 4-4 4-5 4-6 5 5-1 5-2 5-3 5-4 5-5 5-6 6 6-1 6-2 6-3 6-4 6-5 6-6 Select the favorable outcomes for rolling a sum less than five. (5-1) (5-2) (5-3) (5-4) (5-5) (5-6) (1-6) (2-5) (3-4) (4-3) (5-2) (6-1) (1-1) (2-2) (3-3) (4-4) (5-5) (6-6) (1-1) (1-2) (1-3) (2-1) (2-2) (3-1)
(6-6)
Second Roll 1 2 3 4 5 6 1 1-1 1-2 1-3 1-4 1-5 1-6 2 2-1 2-2 2-3 2-4 2-5 2-6 1st 3 3-1 3-2 3-3 3-4 3-5 3-6 Roll 4 4-1 4-2 4-3 4-4 4-5 4-6 5 5-1 5-2 5-3 5-4 5-5 5-6 6 6-1 6-2 6-3 6-4 6-5 6-6 Select the favorable outcomes for rolling double sixes. (6-5) (6-3) (6-6) (6-1)
(1-3) (2-3) (3-1) (3-2) (3-4) (3-5) (3-6) (4-3) (5-3) (6-3)
Second Roll 1 2 3 4 5 6 1 1-1 1-2 1-3 1-4 1-5 1-6 2 2-1 2-2 2-3 2-4 2-5 2-6 1st 3 3-1 3-2 3-3 3-4 3-5 3-6 Roll 4 4-1 4-2 4-3 4-4 4-5 4-6 5 5-1 5-2 5-3 5-4 5-5 5-6 6 6-1 6-2 6-3 6-4 6-5 6-6 Select the favorable outcomes for rolling exactly one three. (1-1) (2-2) (3-3) (4-4) (5-5) (6-6) (1-3) (2-3) (3-1) (3-2) (3-4) (3-5) (3-6) (4-3) (5-3) (6-3) (5-1) (5-2) (5-3) (5-4) (5-5) (5-6) (1-6) (2-5) (3-4) (4-3) (5-2) (6-1)
(5-1) (5-2) (5-3) (5-4) (5-5) (5-6)
Second Roll 1 2 3 4 5 6 1 1-1 1-2 1-3 1-4 1-5 1-6 2 2-1 2-2 2-3 2-4 2-5 2-6 1st 3 3-1 3-2 3-3 3-4 3-5 3-6 Roll 4 4-1 4-2 4-3 4-4 4-5 4-6 5 5-1 5-2 5-3 5-4 5-5 5-6 6 6-1 6-2 6-3 6-4 6-5 6-6 Select the favorable outcomes for rolling a five on the first roll. (5-1) (5-2) (5-3) (5-4) (5-5) (5-6) (1-6) (2-5) (3-4) (4-3) (5-2) (6-1) (1-1) (2-2) (3-3) (4-4) (5-5) (6-6) (1-1) (1-2) (1-3) (2-1) (2-2) (3-1)
(1-3) (2-3) (3-1) (3-2) (3-4) (3-5) (3-6) (4-3) (5-3) (6-3)
Second Roll 1 2 3 4 5 6 1 1-1 1-2 1-3 1-4 1-5 1-6 2 2-1 2-2 2-3 2-4 2-5 2-6 1st 3 3-1 3-2 3-3 3-4 3-5 3-6 Roll 4 4-1 4-2 4-3 4-4 4-5 4-6 5 5-1 5-2 5-3 5-4 5-5 5-6 6 6-1 6-2 6-3 6-4 6-5 6-6 Select the favorable outcomes for rolling exactly one three. (1-1) (2-2) (3-3) (4-4) (5-5) (6-6) (1-3) (2-3) (3-1) (3-2) (3-4) (3-5) (3-6) (4-3) (5-3) (6-3) (5-1) (5-2) (5-3) (5-4) (5-5) (5-6) (1-6) (2-5) (3-4) (4-3) (5-2) (6-1)
A table can be used to show sample space. A tree diagram can be used to show sample space. The counting principle can be used to find the number of outcomes in the sample space.
Select all that apply. Which of the following are true? A table can be used to show sample space. Sample space is the probability of two events happening. A tree diagram can be used to show sample space. The counting principle can be used to find the number of outcomes in the sample space.
18
Suppose you are going to make a sandwich. You have mayonnaise and mustard to spread on the bread. You have white, wheat, and rye bread. You have ham, turkey, and pastrami. How many different sandwiches can you make using one spread, one type of bread, and one type of meat? 18 15 9 8
18
The following table represents the sample space of rolling two number cubes. 1 2 3 4 5 6 1 1-1 1-2 1-3 1-4 1-5 1-6 2 2-1 2-2 2-3 2-4 2-5 2-6 3 3-1 3-2 3-3 3-4 3-5 3-6 4 4-1 4-2 4-3 4-4 4-5 4-6 5 5-1 5-2 5-3 5-4 5-5 5-6 6 6-1 6-2 6-3 6-4 6-5 6-6 How many favorable outcomes are there for the event "rolling exactly one even number"? 27 9 18 16
5%
The table below shows the sample space for spinning a 4-part spinner (labeled A, B, C, D) and then a 5-part spinner (labeled V, W, X, Y, Z). What is the probability of spinning AZ? A B C D V AV BV CV DV W AW BW CW DW X AX BX CX DX Y AY BY CY DY Z AZ BZ CZ DZ 25% 20% 10% 5%
1/9
What is the probability of rolling a sum of 5 if two regular 6-sided number cubes are rolled? 1/5 1/9 5/36 1/6
25%
What is the probability of tossing two coins and having them both land on heads? 33.3% 25% 50% 75%
Students play a simple roulette wheel game. The wheel contains 18 black spaces, 18 red spaces, and 2 green spaces. The students can bet pieces of candy on either landing on black or red on the wheel. If the opposite color or green is landed on they lose.
Which of the following does not represent fair game? During a game of Bunco, each player gets a turn to roll three dice. If the person rolls three of a kind of the same number of the round, they automatically win the round Two people play a game in which they randomly draw numbers from 1 to 12. If the number is even, player 1 wins and if the number is odd player 2 wins. Two people toss a coin to see who gets the ball first in a one-on-one basketball game. Player 1 gets the ball first if the coin lands on heads and player 2 gets the ball first if the coin lands on tails. Students play a simple roulette wheel game. The wheel contains 18 black spaces, 18 red spaces, and 2 green spaces. The students can bet pieces of candy on either landing on black or red on the wheel. If the opposite color or green is landed on they lose.
tree diagram
Which of the following is used to determine the sample space of a compound event? counting principle tree diagram fair game compound event
fair game
a game in which each participant has the same probability of winning
compound event
an event consisting of two or more events that can happen at the same time or one after the other
tree diagram
an organizing tool used to find the sample space for compound events
counting principle
principle that states the number of outcomes for a compound event is found by multiplying the total number of outcomes for each event together
sample space
the set of all possible outcomes for an experiment