Use this information to answer the following questions.

Transcription

1 1 Lisa drew a token out of the bag, recorded the result, and then put the token back into the bag. She did this 30 times and recorded the results in a bar graph. Use this information to answer the following questions. If the bag contains 4 green tokens, 2 red tokens, and 4 purple tokens, how does the theoretical probability of drawing a purple token compare to the experimental probability of drawing a purple token? a. The theoretical probability of drawing a purple token is 2 which is less than the 5 experimental probability of 1. 2 b. The theoretical probability of drawing a purple token is 2 which is greater than 5 the experimental probability of 1. 2 c. The theoretical probability of drawing a purple token is 1, but the experimental 2 probability cannot be determined from the graph above. d. Bar graphs are not appropriate to display data with categories and frequency Green Red Purple

2 2 In a board game, a player spins each of the two spinners shown below. Which of the following lists all of the possible combinations of an even number and either blue or red? a. 1-blue; 3-blue; 5-blue; 7-blue; 1-red; 3-red; 5-red; 7-red b. 1-blue; 2-blue; 3-blue; 4-blue; 5-blue; 6-red; 7-red; 8-red c. 2-red; 4-blue; 6-red; 8-blue; 2-red; 4-blue; 6-red; 8-blue d. 2-blue; 4-blue; 6-blue; 8-blue; 2-red; 4-red; 6-red; 8-red

3 3 The tree diagram below shows the sample space for a problem situation. Which situation below would most likely use this diagram? a. Jessica wore a blue shirt on Monday with a white belt and green pants. On Tuesday she wore a khaki shirt and denim shorts. How many different outfits can she make? b. Randy has three shirts to choose from, a blue, white, or green one. He has two colors of pants, khaki and denim. How many different outfits can he make? c. Betsy has a blue, khaki, and denim scarf in her drawer. She has two jackets in her closet, a white one and a green one. How many different scarf and jackets arrangements can she make? d. Terry s favorite shirt has blue, white, and green stripes on it. He is trying to decide which pants, khaki or denim, to wear to school. How many different ways can he put together his shirt and pants?

4 4 A fair spinner contains 6 equal sections, each with a different color. The table shows the results of spinning the spinner 25 times. Color Number of times Green Red Blue Purple Orange Yellow If the spinner were spun 125 times, how many outcomes would you expect to be purple?

5 5 At James Middle School the grades for one algebra class of 30 students are shown. Based on these results, how many of the 480 algebra students have an A in class? Grade Number A 8 B 6 C 9 D 5 F 2

6 6 In a bag there are 3 yellow marbles, 2 red marbles, and 1 purple marble. Once a marble is selected, it is not replaced. Find the probability of selecting a red marble and then a yellow marble.

7 7 Without looking, Tammy takes a marble out of a bag that contains 10 red marbles, 15 green marbles, and 25 blue marbles. She records its color and returns the marble to the bag. If Tammy repeats this process 90 times, how many times can she expect to pull out a red marble?

8 8 Mrs. Gregory's fourth period class is comparing experimental results to theoretical probabilities. They are using a standard deck of cards and will draw a card from the deck, record what they draw, and replace the card before they draw again. They know that theoretically they should draw a heart 25% of the time. The results of their experiment are in the table below. What is the difference in the theoretical probability of getting a heart and the experimental results recorded in the table? Express your answer as a percent.

9 9 There are 8 girls in a dance class. The girls are represented in the diagrams below by the numbers 1 through 8. If each girl chooses a dance partner, which list shows all the possible combinations of girls in the dance class?

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13 13 If a number cube is rolled twice, what is the probability of getting the number 3 both times?

14 14 There are 4 red, 8 yellow, and 6 blue socks mixed up in a drawer. Once a sock is selected, it is not replaced. Find the probability of reaching into the drawer without looking and choosing 2 blue socks.

15 15 A box contains 150 black pens and 50 red pens. Jose said that the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1. Is he correct? a. Yes, because the probability of not black is 50 and the probability of selecting not red is = b. Yes, because the probability of not black is 50 selecting not red is = and the probability of c. No, because 50 pens are not black and 150 pens are not red. This is much greater than 1. d. No, because the probability of not black is 1 3 and the probability of not red is

16 16 Which of the following events has the most likely probability? a. You roll a six-sided number cube and the number is less than 2. b. You roll two six-sided number cubes and the sum of the numbers is 1. c. A bag contains 3 blue marbles and 3 red marbles. You select a red marble from the bag at random. d. A spinner has 5 equal sections marked 1 through 5. You spin and land on a number less than 5.

17 17 The probability of event A is 1 3 and the probability of event B is 1 4. What can you conclude about the two events? a. The probability of event A is a complement to the probability of event B. b. Neither event is very likely, but event A is more likely to happen than event B. c. The probability of event A is equally likely as the probability of event B. d. The probability of event B is greater than the probability of event A because 1 4 > 1 3.

18 18 A bag contains 3 red chips and 7 green chips. What is the probability of randomly selecting a red chip? A 4 7 because the probability of selecting a green chip is 3 7, and = 4 7. B 3 10 because the probability of selecting a green chip is 7 10, and = C 70% because the probability of selecting a green chip is 30%, and 100% 30% = 70%. D 0.03 because the probability of selecting a green chip is 0.07, and = 0.03.

19 19 Ray and Shannon are playing a game. The probability of Ray winning the game is If the game cannot end in a tie, what is the probability of Shannon winning the game? A B 9 25 because the probability of Ray winning the game is 9 25, and = because the probability of Ray winning is 0.36 = C 0.74 because Ray s probability and Shannon s probability must equal 1, and = 1. D 9 16 because the probability of Ray winning is 0.36, and = 9 16.

20 20 Below are pairs of simple events. Which of the following correctly describes the event and its complement? A The probability of rolling a composite number on a six-sided number cube is 1 3. Rolling a prime number is its complement, = 2 3. B The probability of flipping tails on a fair coin is 50%. Flipping heads on the fair coin is its complement, 100%-50%=50%. C The probability of selecting a weekday is 5. Friday is sometimes considered part of the 7 weekend, so selecting the complement to a weekday would be = D The probability of choosing a vowel from the alphabet is The probability of selecting a consonant its complement, 26 5 = 21.

21 21 The spinner below is used in a board game to determine where players move a game piece. What is the probability of spinning the complement of spinning blue? A 1 4 because the probability of spinning green is equal to the probability of spinning blue. B 2 3 because the probability of spinning blue is 1 3, and = 2 3. C 5 because the complement of spinning blue is spinning red. 12 D 3 4 because the probability of spinning blue is 1 4, and = 3 4.

22 22 A gumball machine contains gumballs of five different colors: 36 red, 44 white, 15 blue, 20 green, and 5 orange. The machine dispenser randomly selects one gumball. Which of the following statements is false? A The probability of not green is = 5 6. B The probability of not orange is 1 - P(orange) = = C The probability of blue is 1 6. D The probability of a color other than red, white or blue is = 5 24.

23 23 The diagram below shows all of the possible sums when rolling two six-sided number cubes. Two six-sided number cubes are tossed, and the sum is recorded. What is the probability of rolling the complement of a sum greater than 7? a because the probability of rolling a sum greater than 7 is = b because the probability of rolling a sum greater than 7 is 5 12, so = c. 5 6, because the probability of rolling a sum of 7 is 1 6, so = 5 6. d. 1, because the probability of rolling a sum greater than 7 is equal to the probability of rolling a sum less 2 than 7.

24 24 Gabe and Sasha take turns spinning the spinner below to see who will get to use their family's shared computer. If the spinner lands on red, Gabe gets computer time first. If the spinner lands on a color other than red, Sasha gets to use the computer first. Which of the following statements below is correct? a. If Gabe spins first, the outcome of his spin has an effect on the outcome of Sasha s spin. b. Gabe and Sasha have an equally likely chance of getting to use the family computer first. c. Gabe has a greater likelihood of getting to use the computer first because 1 > d. Sasha is more likely to get the computer first because she can land on 3 of the color choices, while Gabe 4 can only land on 1 of the color choices and 3 >

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