Independent Probability: Martin’s Cereal Challenge
Name
Period
Determining probabilities can help you understand past events and make decisions about future events.
Probability is the chance that some event will happen. It is the ratio of the number of ways a certain event can
occur to the number of possible outcomes. The probability of an event occurring is written with a capital P
followed by the specific event in parentheses.
P(event) =
# of ways that event can occur _
Total number of possible outcomes
Theoretical probability is the probability of an event occurring, based on mathematical calculations.
Experimental probability is the probability of an event occurring, based on the frequency of outcomes during
an experiment.
CEREAL MATH
Martin, an eighth grader, always has cereal for
breakfast. He likes Cocoa Puffs cereal so much that he wants
to eat it every morning. Martin’s mother wants him to eat
VS.
Grape Nuts at least some mornings because it is more
nutritious than Cocoa Puffs.
Martin and his mother have come up with a fun way to
determine which cereal Martin will have for breakfast. Each morning, Martin flips a coin. If the coin comes up
heads, he will have Cocoa Puffs. If it comes up tails he will have Grape Nuts.
EXPLORATION
How often will Martin eat Cocoa Puffs in June? We can explore the probability that Martin will get to
eat Cocoa Puffs vs. Grape Nuts by conducting an experiment in which we flip a coin 30 times.
1. Fill in the data tables on the back of this sheet to help collect and organize your data.
 For each day, record the result of the flip (H or T) and the percent of heads to date. For
example, if it is June 5th and Martin has gotten heads a total of 3 times, the percent of heads to
date would be 3/5 = 60%.
 Answer the questions below once you have completed the data tables.
2. Use this data to make a coordinate graph (on graph paper) with the days from 1 to 30 on the x-axis
and the percent of heads to date on the y-axis.
3. As you added more and more data, did the fraction of heads get closer or further from ½? Explain your
answer.
4. Based on what you found for June, how many times would you expect Martin to eat Cocoa Puffs in
July?
5. Based on what you found for June, how many times would you expect Martin to eat Cocoa Puffs in an
entire year (1 year = 365 days)?
6. Martin’s mother told him that the chances of flipping a coin and getting heads is ½. Does this mean if
you flip a coin twice you should expect to get one head and one tail? Explain your reasoning.
Experimental Results
June
Number
of Heads
Number
of days
Percent
of
Heads to
Date
Number
of Heads
Number
of days
Percent
of
Heads to
Date
Number
of Heads
Number
of days
Percent
of
Heads to
Date
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30