SINGLE EVENT PROBABILITY
Introduction
The chance of some event happening; such as flipping a coin and having it land with the head side up, or rolling a "four" on a single die, is called probability. Probability is expressed as a fraction. The probability of an event occurring equals the number of ways the event can occur divided by the total number of events possible.
A die has only one way to land with a "four" showing, but has the possibility to land on any of six sides. Therefore, the probability of a "four" showing on the die after one throw is 1/6. That is, you will probably see a "four" thrown once out of six throws of the die.
Procedure and Data
A. Calculating probability
1. If you flip a coin, what is the probability that it will land heads?
2. If you pull a card from a regular bridge deck of cards, what is the probability that you will draw an ace? (Remember to reduce your fraction.)
3. If there are 3 red crayons and 5 blue crayons in a box, find each of the following probabilities:
a. drawing out a red crayon? 
b. drawing out a blue crayon? 
c. drawing out a green crayon? 0
d. drawing out either a red or blue crayon? 1
e. after drawing out a blue crayon, what is the probability of drawing another
blue crayon on the next draw? 
f. after drawing out a red and a blue crayon, what is the probability of drawing
a red on the next draw? 
B. Demonstration of probability through a hands-on activity
Probability is a prediction or guess (hypothesis) of whether a particular event will occur. If you had to guess how many times a coin would land heads out of 10 tosses, you would most likely guess that heads would be displayed 5 times. But, you know from experience that when you flip a coin, there usually is not an equal number of heads as tails. Sometimes the coin lands tails many times in a row without a head being tossed. In order for probability to be demonstrated, many more than 10 observations must be tracked. In the scientific world, keeping track of your observations is known as data collection. The results of an experiment must be collected repeatedly so that reporting the information becomes statistically accurate. When a scientist is able to obtain similar data when the same experiment is performed, the experiment and results are considered more reliable.
Data Collection: One partner will toss a coin fifty times and have his/her partner record the results using tally marks in the table below. Then reverse rolls so that the person who did the tallying will now flip the coin (each partner will therefore have a record of his/her own 50 tally marks in the table below).
Heads Tails
Total heads Total tails Total tosses 50
Data Interpretation:
a. What is the total number of times you flipped heads? answers will vary
b. What is the total number of times you flipped tails?
answers will vary
c. Are the number of heads different than the number of tails? they probably are
d. What fraction of your total flips were heads?
answers will vary
e. What fraction of your total flips were tails?
answers will vary
f. Are your two fractions equal?
probably not
Class activity: With your teacher's help, combine your data with the class results in a table on the board, and record the class totals in the table below.
a. What is the total number of times the class flipped heads?
answers will vary
b. What is the total number of times the class flipped tails?
answers will vary
c. Are the number of heads different than the number of tails?
They are probably not equal, but more equal than in "Data Interpretation" above. Students may have an easier time comparing these numbers if they convert to decimals before making the comparison.
d. What fraction of the total class flips were heads?
answers will vary
e. What fraction of the total class flips were tails?
answers will vary
f. Are these class fractions equal?
probably not equal, but more equal than in "Data Interpretation" above.
g. Which set of fractions are closer to each other, your individual set or the class fractions?
the class set is probably closer in value