Exam 27: Quantifying Uncertainty

If you flip a fair coin 20 times, you will always get 10 tails.

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.

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.)

Why isn't the following statement a correct use of the word "probably"? Since the new arena opened, some event has probably been sold out.

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.

"In situation X, the probability of Y happening is $\frac { 2 } { 3 }$ ." What does that mean?

Experiment: Spin the spinner below twice, recording the color each time. A) What outcome(s) is/are in the event "get different colors"? (Not the whole sample space, just the event.) B) How would you determine the experimental probability of the event in part A? (Give a complete explanation, not just part of one.)

In a particular experiment with only three outcomes, X, Y, and Z, the probability of X is $\frac { 3 } { 16 }$ and the probability of Y is $\frac { 1 } { 4 }$ . What is the probability of Z?

"You wonder what the chances were that the team's record would be five wins and one loss at this time last year" is a probabilistic situation.

If a fair die is rolled once, the probability that you get a four, given that the die comes up an even number, is one-third.

"With our spinner, our group got probability of red = $\frac { 5 } { 200 }$ , probability of green = $\frac { 50 } { 200 }$ , and probability of yellow = $\frac { 245 } { 200 }$ ." What do you know without seeing the spinner?

If you flip a fair coin 2000 times, you will always get 1000 heads.

If Y is impossible, the probability of not Y is one.

A bag has only red balls and green balls. The experiment is to draw one ball from the bag without looking. What does it mean to say, "The probability of getting a green ball is 40%"?

A) The theoretical probability of getting red for the spinner below is ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ. (The spinner is a regular pentagon.) B) What does your answer in part A mean? C) Tell how you would find the experimental probability for getting red for the spinner above if you wished to check your theoretical probability.

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

Why isn't the following statement a correct use of the word "probably"? Last year, a good player probably scored four touchdowns in some game.

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

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?

Suppose you have a brand new quarter. What does it mean to say, "The probability of getting heads when I toss the quarter is 50%"?