Sample Space (practice)~ amdm

A computer is programmed to generate a sequence of three digits, where each digit is either 0 or 1, and each of these is equally likely to occur. Construct a sample space that shows all possible three-digit sequences of 0s and 1s and then find the probability that a sequence will contain at least one 0. a. 000, 001, 010, 011, 100, 101, 110, 111; P(at least one 0) = 7/8 b. 000, 001, 010, 100, 101, 110 ; P(at least one 0) = 6/6 c. 100, 101, 110, 111; P(at least one 0) = 3/4 d. 000, 001, 010, 011; P(at least one 0) = 4/8 = 1/2

A. 000, 001, 010, 011, 100, 101, 110, 111; P(at least one 0) = 7/8

If you roll a die three times, how many different sequences are possible? a. 6^3 = 216 b. 3^6 = 216 c. 3^6 = 729 d. 6^3 = 729

A. 6^3 = 216

Suppose you flip a penny and a dime. Use the following table to display all possible outcomes. If each single outcome is equally likely, you can use the table to help calculate probabilities. What is the probability of getting one head and one tail, on either coin? a. P(1 head and 1 tail) = 2/4 = 1/2 b. P(1 head and 1 tail) = 3/4 c. P(1 head and 1 tail) = 4/4 = 1 d. P(1 head and 1 tail) = 1/4

A. P(1 head and 1 tail) = 2/4 = 1/.2

If a random experiment consists of rolling a six-sided die 10 times, how many individual outcomes make up the sample space, and what is the probability of getting all sixes? a. There are 10^6 possible outcomes, only one of which is all sixes, so the probability of getting all sixes is (1/10)^6 = 0.000001 b. There are 6^10 possible outcomes, only one of which is all sixes, so the probability of getting all sixes is (1/6)^10 = 0.0000000165 c. There are 10^6 possible outcomes, only one of which is all sixes, so the probability of getting all sixes is (1/6)^10 = 0.0000000165 d. There are 6^10 possible outcomes, only one of which is all sixes, so the probability of getting all sixes is (1/10)^6 = 0.000001

B. There are 6^10 possible outcomes, only one of which is all sixes, so the probability of getting all sixes is (1/6)^10 = 0.0000000165

You have four sweaters, five pairs of pants, and three pairs of shoes. How many different combinations can you make, wearing one of each? Explain your answer. a. 4 * 5+ 3 = 23 b. 4 * 5 = 20 c. 4 * 5 * 3 = 60 d. 4 + 5 + 3 + 12

C. 4 * 5 * 3 = 60

Consider the following experiment: A card is picked at random from a standard deck of 52 cards. What is the sample space of the experiment? What is the probability of drawing a red card from the deck if 26 of the cards are red? a. 26 possible outcomes; P(red card) = 1/26 b. 52 possible outcomes; P(red card) = 25/52 c. 52 possible outcomes; P(red card) = 1/2 d. 26 possible outcomes; P(red card) = 4/13

C. 52 possible outcomes; P(red card) = 1/2

If a coin is flipped four times, find the probability distribution for the number of heads. Listed below are four charts. Choose the chart that best evaluates the data. a. Chart A c. Chart C b. Chart B d. Chart D

C. Chart C

In a single experiment, a die is tossed and a spinner with the letters A, B, and C is spun. Each letter is equally likely. Draw your sample space and then find the probability of getting a 2 or a B. a. The sample space is 9. The probability of getting a B is 1/9 b. The sample space is 18. The probability of getting a 2 or a B is 18/8 = 9/4 c. The sample space is 18. The probability of getting a 2 or a B is 8/18 = 4/9 d. The sample space is 9. The probability of getting a 2 or a B is 8/18 = 4/9.

C. The sample space is 18. The probability of getting a 2 or a B is 8/18 = 4/9

A fair coin is flipped three times. The sample space for this experiment is as follows: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} Which table represents the experiment and the probabilities for number of heads? a. Table A b. Table B c. Table C d. Table D

D. Table D

In a single experiment, a die is tossed and a spinner with the letters A, B, and C is spun. Each letter is equally likely. Find the sample space and then find the probability of getting a 2 on the die and a B on the spinner. a. The sample space is 18. The probability of getting 2 and B is 1/18 b. The sample space is 9. The probability of getting 2 and B is 1/9 . c. The sample space is 18. The probability of getting 2 and B is 1/9 d. The sample space is 9. The probability of getting 2 and B is 1/18

a. The sample space is 18. The probability of getting 2 and B is 1/18.