Probability Assignment

Transcription

1 Name Probability Assignment Student # Hr 1. An experiment consists of spinning the spinner one time. a. How many possible outcomes are there? b. List the sample space for the experiment. c. Determine the probability of the spinner landing on a number or a letter. List the outcomes in this event. Then, calculate the probability. d. Determine the probability of the spinner landing on a consonant or an odd number List the outcomes in this event. Then, calculate the probability. 2. An experiment consists of tossing a coin 50 times. a. List the sample space for the experiment. b. How many times do you expect the coin to land on each side? c. Determine the theoretical probability of heads and the theoretical probability of tails. d. Results from tossing the coin 50 times are shown in the table. Calculate the experimental probabilities to complete the table. Side Tally Total Probability Heads 23 Tails 27 e. Compare the experimental probabilities to the theoretical probabilities you calculated in part (c). Are they the same or different? Explain why.

2 3. You have 100 decks of standard playing cards. Each deck contains 52 cards, and each card is one of four suits clubs, diamonds, hearts, or spades. a. What are the possible outcomes for drawing a club? b. What is the P(face card). c. What is the P(ace) d. What is the P(heart) e. Would it be better to simulate 25 trials or 100 trials? Explain. 4. You spin each spinner once. On the spinners, R represents red, B represents blue, G represents green, Y represents yellow, and P represents purple. a. Create an organized list of all the possible outcomes. b. What is the probability that both spinners will land on the same color? c. What is the probability that the first spinner will land on Red and the second spinner will land on Purple? d. What is the probability that the first spinner will land on Red or the second spinner will land on Purple?

3 5. Keme is learning probability in middle school while her little brother, Cade, is learning arithmetic in first grade. Keme uses a six-sided number cube to help Cade learn how to add one-digit numbers. She rolls two cubes, numbered 1 through 6, and Cade adds up the two numbers on the faces. a. Use a tree diagram to determine all the possible outcomes. List the sum at the end of each branch of the tree. b. Complete the probability model for rolling 2 six-sided number cubes and finding the sum of the faces. Sum Probability c. P(sum of 7) d. P(sum of 11) e. P(sum is an even number). f. P( sum is more than 5) 6. Describe an event (not from our notes), that would be impossible, equally likely, and certain to happen. a. Impossible b. Equally Likely c. Certain

4 Probability Assignment Answer Section 1. ANS: a. There are 8 possible outcomes. b. {A, B, C, D, 1, 2, 3, 4} c. Outcomes: A, B, C, D, 1, 2, 3, 4 d. Outcomes: B, C, D, 1, 3 PTS: 1 REF: 16.1 NAT: 7.SP.5 TOP: Pre Test KEY: outcome experiment sample space event simple event probability equally likely 2. ANS: a. {heads, tails}

5 b. heads: 25 times tails: 25 times c. d. Side Tally Total Probability Heads 23 Tails 27 e. The probabilities are different. Experimental probability is determined from doing an experiment. You may not always get the same results as what is expected from the theoretical probability when you do an experiment. PTS: 1 REF: 16.2 NAT: 7.SP.5 7.SP.6 7.SP.7.a 7.SP.7.b TOP: Pre Test KEY: experimental probability 3. ANS: a. club, diamond, heart, spade b. Designate an integer from 1 to 4 to represent choosing a club. Then, have the spreadsheet program generate many random integers between 1 and 4, inclusive. Each random number represents a trial. c. I would use the function RANDBETWEEN. d. I will use 1 and 4 because there are four suits in a deck of cards. e. It would be better to simulate 100 trials. The experimental probability approaches the theoretical probability as the number of trials increases. PTS: 1 REF: 16.5 NAT: 7.SP.6 7.SP.7.a 7.SP.7.b TOP: Pre Test KEY: spreadsheet 4. ANS: a. (R, R), (R, B), (R, P), (R, Y) (B, R), (B, B), (B, P), (B, Y) (G, R), (G, B), (G, P), (G, Y) b. There are 2 outcomes for this event: (R, R) and (B, B).

6 P(same color), or c. There is 1 outcome for this event: (R, P). P(R on 1st and P on 2nd) d. There are 6 outcomes for this event: (R, R), (R, B), (R, P), (R, Y), (B, P), and (G, P). P(R on 1st or P on 2nd), or PTS: 1 REF: 17.3 NAT: 7.SP.7.a 7.SP.7.b 7.SP.8.a 7.SP.8.b TOP: Pre Test KEY: compound event 5. ANS: a. b. The possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. c. Number of Heads Probability d. P(1 or 2 heads), or e. The complementary event for no heads is 1 or 2 or 3 heads. P(1 or 2 or 3 heads) P(1) P(2) P(3) P(1 or 2 or 3 heads) 1 P(0 heads) PTS: 1 REF: 17.2 NAT: 7.SP.7.a 7.SP.7.b 7.SP.8.a 7.SP.8.b TOP: Post Test KEY: tree diagram complementary events