Question 1

Experiment: Spin each of the two spinners below and record the color on each.  
A) Give the sample space for the experiment.
B) Describe an event for the experiment above, and tell how one would determine the experimental probability for the event.

Accepted Answer

The answer of Experiment: Spin each of the two spinners...

Question 2

In an experiment with two outcomes, each outcome must have probability 50%.

Accepted Answer

In an experiment with two outcomes, the probabilities of the outcomes must sum to 100%, but each outcome does not necessarily have a probability of 50%. The probabilities can vary as long as they sum to 100%.

Question 3

For a three-color spinner with P(red) = $\frac { 1 } { 4 }$ and P(white) = $\frac { 1 } { 8 }$ , P(blue) could be $\frac { 7 } { 8 }$ .

Accepted Answer

The sum of probabilities for all outcomes must equal 1. Given P(red) = 1/4 and P(white) = 1/8, the sum is 1/4 + 1/8 = 3/8. Therefore, P(blue) = 1 - 3/8 = 5/8, not 7/8.

Question 4

The theoretical probability and the experimental probability of an event will be the same.

Accepted Answer

Theoretical probability is based on the possible outcomes in a perfect scenario, while experimental probability is based on actual results from an experiment, which can vary due to chance and real-world factors.

Question 5

In an experiment with four outcomes, P, Q, R, and S, the probability of P is  $\frac { 1 } { 3 }$ , the probability of Q is $\frac { 1 } { 2 }$ , and the probabilities of R and S are equal to each other. What is the probability of S? 
A) $\frac { 1 } { 12 }$

B) $\frac { 1 } { 6 }$

C) $\frac { 3 } { 10 }$

D) $\frac { 5 } { 6 }$

Accepted Answer

The answer of In an experiment with four outcomes, P,...

Question 6

Design a simulation for a spinner that would allow a simulation of a birth happening during any of the 12 months of the year with equal probabilities. Describe how you would carry out the simulation.

Accepted Answer

The answer of Design a simulation for a spinner that...

Question 7

Design an experiment based on drawing balls from a bag that would allow for the simulation of a success (getting well) for a sick person undergoing a treatment, with probability of success 0.6.

Accepted Answer

The answer of Design an experiment based on drawing balls...

Question 8

You give a child the choice of drawing from two bags of balls. The child wins if he/she draws a red ball. Bag 1 has four red balls and seven green balls; bag 2 has two red balls and three green balls. Which bag gives the child a better chance of winning (or are the chances the same)? Please explain.

Accepted Answer

The answer of You give a child the choice of...

Question 9

Simulating an experiment with randomly generated numbers gives experimental probabilities.

Accepted Answer

Simulating an experiment with randomly generated numbers allows for the approximation of experimental probabilities based on the outcomes observed from the simulation.

Question 10

You may wish to use a table of randomly generated numbers efficiently to simulate this experiment.
Experiment: Draw a ball from a bag that has 13 black balls (B), 5 red balls (R), and 2 green balls (G), and note its color.
A) Tell what your code would be if you use two-digit random numbers. Use an efficient code, omitting as few numbers as you can.
00 01 02 03 …………………………………………………… 97 98 99
B) Use the following randomly selected digits to simulate the experiment above 15 times.
10394 8854 96029 711517 87601 71480 49210 81314 84069 64343 65909 23870
C) What is the theoretical probability of getting a red ball?
D) What is the probability of getting a red ball from your simulation in part B?
E) Explain the difference between the answer in part C and the answer in part D.

Accepted Answer

The answer of You may wish to use a table...

Question 11

You may wish to use randomly selected digits efficiently to simulate this experiment.
Experiment: Draw a ball from a bag that has 11 black balls (B), 5 red balls (R), and 4 green balls (G), and note its color.
A) Tell what your code would be if you use two-digit numbers. Use an efficient code, omitting as few numbers as you can.
00 01 02 03 …………………………………………………… 97 98 99
B) Use the following from our table of randomly selected digits to simulate the experiment above 15 times efficiently.
11517 87601 71480 49210 81314 84069 64343 65909 23870 10394 8854 96029
C) What is the theoretical probability of getting a green ball?
D) What is the probability of getting a green ball from your simulation in part B?
E) Explain the difference between the answer in part C and the answer in part D.

Accepted Answer

The answer of You may wish to use randomly selected...

Question 12

One basketball player hits 46% of her shots.
A) Give a code for hits and a code for misses so that one could use the table of randomly selected digits to simulate shots by the player.
B) If you use your code two times to simulate 300 shots each time, will you get the same results both times? Explain why/why not.

Accepted Answer

The answer of One basketball player hits 46% of her...

Question 13

Ten percent of the time a student comes to my office, he or she leaves something behind. Estimate the probability, using a simulation model and the two-line random number table given, that exactly one out of the next four students will leave something behind. (Use 20 samples.) Show how you came to your answer.
13366527640249714202741725877065348241154427796735
96734100241534687634091232686745732531809874574312

Accepted Answer

The answer of Ten percent of the time a student...

Question 14

A) Design a table of randomly selected digits simulation for the following experiment.
Spin a spinner that is $\frac { 1 } { 4 }$ red, $\frac { 1 } { 2 }$ green, and the rest white, and notice the color. 
B) Do your simulation 20 times. Record enough so that your work can be checked.
C) According to your simulation, what is the probability of green?

Accepted Answer

The answer of A) Design a table of randomly selected...

Question 15

An experimental rocket will be launched. The launch has an 89% probability of success. With a table of randomly selected digits, what would be an efficient code for success and an efficient code for failure for simulating the launch?

Accepted Answer

The answer of An experimental rocket will be launched. The...

Question 16

Simulating an experiment with software gives theoretical probabilities.

Accepted Answer

The answer of Simulating an experiment with software gives theoretical...

Question 17

Experiment: Toss four dishonest coins-penny, nickel, dime, quarter-with P(H) = 0.6 for each coin. A computer produced the table below for a simulation of the whole experiment 8000 times.  
A) In the HHHH line (the first line in the body of the table), how did the computer calculate to get 0.1291?
B) What is the probability of at least one tail (T), according to this simulation?

Accepted Answer

The answer of Experiment: Toss four dishonest coins-penny, nickel, dime,...

Question 18

Experiment: Toss four dishonest coins-penny, nickel, dime, quarter-with P(H) = 0.6 for each coin. A computer produced the table below for a simulation of the whole experiment 8000 times.  ​ 
A) In the HHTT line (the fourth line in the body of the table), how did the computer calculate to get 0.0621?
B) What is the probability of at least one head (H), according to this simulation?
​

Accepted Answer

The answer of Experiment: Toss four dishonest coins-penny, nickel, dime,...

Question 19

The computer outputs below are for 3000 trials of spinning the spinners. Explain the differences in the outputs between the two spinners. (Event (O) means the outcomes are ordered.)

Accepted Answer

The answer of The computer outputs below are for 3000...

Quiz 27: Quantifying Uncertainty

Experiment: Spin each of the two spinners below and record the color on each. A) Give the sample space for the experiment. B) Describe an event for the experiment above, and tell how one would determine the experimental probability for the event.