Download Probability of a Kiss (random sampling, long run relative frequency

Core Standards
7.SP.1, 2, 5, 6
Introduction to Statistics
Class Activity Probability of a Kiss
Teacher version, student version below
When you toss a coin, it will either land heads or tails. That isn’t very interesting. But suppose you
toss a Hershey’s Kiss in the air, and then observe how it lands. That is much more interesting! And
you can eat the Kiss!
The sample space for tossing a Kiss has two possible outcomes: S = {base, side}. “Base” means
the Kiss landed on the flat base, and “side” means the Kiss landed on its side.
What is the probability for each outcome? Ha! That was a trick question. We don’t know the
answer. First we must do an experiment, and then calculate the experimental probability that the
Kiss will land on its base, P(B).
1. Define “long run relative frequency”. The probability of an outcome obtained after many
trials.
2. Make a guess for the probability that a Kiss tossed in the air will land on its base:
P(B) = Student answers will vary, most students might think the Kiss will land more frequently on
the base, but actually it will land more frequently on the side. There is more surface area on side
than the base. In past trials done by students, the probability of landing on the base was always less
than .5, sometimes about .3
3. Record the results of your experiment in the table after each toss, and calculate the
experimental probability after each trial. Notice that the probabilities are calculated from:
(Base running total)/(trial number).
4. Make a plot of your results by plotting the trial number against the experimental probability.
Connect the points from trial 1, to trial 2, to trial 3,…and end with trial 30.
Outcome
(B or S)
# of times on Base
(running total)
Trial Number
Experimental
Probability
Outcome
(B or S)
1
2
3
4
5
6
7
8
9
10
# of times on
Base
(running total)
Trial Number
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Experimental
Probability
Outcome
(B or S)
# of times on
Base
(running total)
Trial Number
Experimental
Probability
5. What was the experimental probability of a Kiss landing on its base after 30 trials?
P(B) = The answer can be found with trial 30. Or can it be read from the plot.
Compare your experimental probability to the guess you made at the beginning of the
activity. How close was your guess?
6. Compare the value for the experimental probability at Trial 2, compared to Trial 20. Which
value was closer to the final experimental value at Trial 30? It is most likely that end value
is closest to Trial 20. There are limited possible experimental values at Trial 2: either 1, .5,
or 0. Since there are limited experimental probabilities at Trial 2, isn’t it also true that there
are limited experimental probabilities for trial 30? Yep! But that list is pretty long, and the
extreme values (all trials landed on the base, or all trials landed on the side) are unlikely.
7. Examine the appearance of the plot. Why was the plot was so variable at the beginning
compared to at the end? Allow time for discussion. Look for: when the trial number is
small, each new trial makes a big difference in the experimental probability. But near the
end, the new trials are averaged in with many other trials, so it doesn’t change as much, and
hopefully is closer to the theoretical probability.
8. Why is it important to perform many trials in an experiment, and not just a few? Refer to
the discussion in previous answer. Also, discuss fact that the theoretical probability for this
activity will never be known. In life, theoretical probabilities are rarely known. For
instance, you never really know for sure that you have a fair coin, it just seems likely!
Questions? Contact:
Joyce Smart [email protected]
Chelsea Parrish [email protected]
Name ________________________
Class Period ______
Class Activity: Probability of a Kiss
When you toss a coin, it will either land heads or tails. That isn’t very interesting. But
suppose you toss a Hershey’s Kiss in the air, and then observe how it lands. That is
much more interesting! And you can eat the Kiss!
The sample space for tossing a Kiss has two possible outcomes: S = {base, side}. “Base” means
the Kiss landed on the flat base, and “side” means the Kiss landed on its side.
What is the probability for each outcome? Ha! That was a trick question. We don’t know the
answer. First we must do an experiment, and then calculate the experimental probability that the
Kiss will land on its base, P(B).
1. Define “long run relative frequency”.
2. Make a guess for the probability that a Kiss tossed in the air will land on its base:
P(B) =
3. Record the results of your experiment in the table after each toss, and calculate the
experimental probability after each trial.
4. Make a plot of your results by plotting the trial number against the experimental probability.
Connect the points from trial 1, to trial 2, to trial 3,…and end with trial 30.
Outcome
(B or S)
# of times on Base
(running total)
Trial Number
Experimental
Probability
1
2
3
4
5
6
7
8
9
10
Outcome
(B or S)
# of times on
Base
(running total)
Trial Number
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Experimental
Probability
Outcome
(B or S)
# of times on
Base
(running total)
Trial Number
Experimental
Probability
5. What was the experimental probability of a Kiss landing on its base after 30 trials?
P(B) =
Compare your experimental probability to the guess you made at the beginning of the
activity. How close was your guess?
6. Compare the value for the experimental probability at Trial 2, compared to Trial 20. Which
value was closer to the final experimental value at Trial 30?
7. Examine the appearance of the plot. Why was the plot was so variable at the beginning
compared to at the end?
8. Why is it important to perform many trials in an experiment, and not just a few?
Probability of a Kiss: Graph your results below. Draw lines between the points when you are finished.
Experimental Probability
Trial Number
Homework
Choose an object that has will have two outcomes when tossed, such as a spoon, a marshmallow, or
a thumb tack.
Use the techniques from the class activity to find the experimental probability that the object will
land on one of the sides.
Plot the data, using the same graph as the class activity. However, plot the outcomes for the
homework using a different color, and then label it.
Write a few paragraphs summarizing the outcome of your experiment.