1
Introduction to Probability
Let us consider the following experiment with the spinner represented in the figure.
Every time we spin the arrow the outcome will be that the arrow will land on one of the
eight sectors, which are identified by colors, letters or numbers. Using the figure, answer
the following questions.
1. What fraction of the time will the arrow land on a blue sector?________
2. What fraction of the time will the arrow land on a green sector?________
3. What fraction of the time will the arrow land on a blank sector (a sector with no
numbers nor letters)?________
4. What fraction of the time will the arrow land on a sector with letters on it?______
5. What fraction of the time will the arrow land on a sector with numbers on it?____
Project AMP
A Quesada Director Project AMP
2
6. Explain the reasoning you used to answer the previous questions.
7. What fraction of the time will the arrow land on a sector that contains both
numbers AND letters? _________
8. What fraction of the time will the arrow land on a sector that is either blue OR
green? ________
In a given experiment, the “fraction of the time,” known as the probability, for the
occurrence of a particular event is obtained by the quotient of the total number of
favorable outcomes over the total number of possible outcomes.
9. In general, what kinds of values are possible when a probability is being
evaluated: Negative numbers? Proper fractions? Improper fractions? Numbers
between 0 & 1? Percentages over 100%? (Choose all that apply)
10. In problems #1 & #2 you found the separate probabilities for “blue” and for
“green”. How does your answer to #8 compare to your answers to #1 & #2? Do
you think this pattern will always be true when you find the probability of one
thing OR another?
11. Check your intuition in #10 by figuring out the probability that the arrow will land
on a sector that either contains numbers OR letters. _________ How does this
answer compare to the sum of the individual probabilities of landing on a sector
that contains letters (#4) and of landing on a sector that contains numbers (#5).
Did the pattern hold?
12. Why did the “addition trick” work in #10, but not in #11? What is different about
these two problems? Can you think of a rule that would work in both cases?
(Hint: Consider your answer to # 7.)
Project AMP
A Quesada Director Project AMP
3
13. You could find the probability that it will land on a sector that is not blank (that
is, it either contains numbers or letters) by counting the pieces that aren’t blank
(7) and dividing by the total number of pieces (8). Can you think of another way
to figure the probability that your piece is not blank, since you already know the
probability that it will land on a blank sector is 1/8.
14. Based on your answer to #10, make up a rule that could be used to find the
probability that some particular result won’t happen, if you already have figured
out the probability of that the particular result will happen.
15. Use your rule from #11 to figure out the probability that you will not win the
grand prize in a sweepstakes, if the chance of winning is 1/1,000,000.
Project AMP
A Quesada Director Project AMP
4
Suppose you have a cousin that wants to come visit you one day in August. The only
problem is that your cousin is very indecisive and cannot make up his mind as to which
day he will come. Suppose the following is a calendar for the month of August.
Sun. Mon. Tues. Wed. Thurs.
1
4
5
6
7
8
11
12
13
14
15
18
19
20
21
22
25
26
27
28
29
Fri.
2
9
16
23
30
Sat.
3
10
17
24
31
He has decided to put the numbers 1 through 31 in a hat and draw out the date that he will
come visit you. Use the ideas that you have developed thus far in this lesson to figure out
the following probabilities:
1. … that he will choose a Thursday ___________
2.
… that he will choose a Tuesday ____________
3. … that he will choose a Tuesday or a Thursday ____________
4. ... that he will choose a date during the week of August 18-24 ____________
5. …that he will not choose a Wednesday ____________
6. … that the day in August that he chooses will be an odd numbered day _______
7. …that he will choose an odd numbered Thursday ___________
8.
… that he will choose either a Thursday or an odd numbered day ___________
Project AMP
A Quesada Director Project AMP