Probability
Probability - Simple Events
Vocabulary
 Sample Space: set of all possible outcomes
Basic Steps for Probability Problems
 Find all possible outcomes in organized manner – exhaustive listing
 Determine which of possibilities yield specified result – winners
Experimental Probability = P(event) =
Theoretical Probability = P(A) =
# winners
# possibilities
m
where n is likely outcomes and m is number of times A occurs
n
Key Concepts:
 If event is certain to not occur, then probability is 0 or 0%.
 If event is certain to occur, then probability is 1 or 100%.
Probability of point within rectangle
 Find the area of the entire/large rectangle (# of possibilities)
 Find the area of smaller rectangles (# of winners)
Geometric Probability
 Find the area of the entire/large circle (# of possibilities)
 Find the area of smaller circle (# of winners)
Simple Events Examples
1. A class tossed coins and recorded 161 heads and 179 tails. What is the experimental probability of
heads? Of tails?
161
179
Total =161 + 179 = 340
P(H) =
= 47%
P(T) =
=53%
340
340
2. Find the theoretical probability of getting a prime number when you roll a number cube.
Prime number outcomes are 1, 3, 5; therefore there are 3 outcomes resulting in prime number
There are 6 likely outcomes.
3 1
P(prime #) = =
6 2
3. If coin is flipped once, what is the probability of it landing heads?
# of possibilities = 2 (heads, tails)
# of winners = 1 (heads)
1
P(H) =
2
4. A point within large rectangle is chosen at random. Find probability that the point is in smaller
rectangle.
# of possibilities = area of entire rectangle = 10 * 40 = 140
# of winners = area of smaller rectangle = 3 * 4 = 12
12
Probability =
140
1
Rev B
Probability
Simple Events Practice
5. A bowl contains 12 slips of paper, each with a different name of a month. Find probability that slip
selected at random from bowl has name of month that starts with letter J.
6. Suppose that a dart lands at random on the
dartboard shown at the right. Find each
theoretical probability.
a. Dart lands in bull’s-eye.
b. Dart scores at least 10 points.
c. Dart scores less than 10 points
Probability - Multiple Events
Dependent Events:
 Events influence one another.
Independent Events:
 Events don’t influence one another.
 Find probability of the 1st event, find the probability of 2nd event and then multiply the two together.
 If A and B are independent events, then P(A and B) = P(A) * P(B)
Mutually Exclusive Events:
 Two events that cannot happen at the same time
 If A and B are mutually exclusive, then P(A or B) = P(A) + P(B).
 If A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) – P(A and B)
Classify Events Examples – Classify as either dependent or independent
7. Spin a spinner. Then, select a marble from a bag that contains marbles of different colors.
8. Select a marble from a bag that contains marbles of two colors. Put the marble aside, and select a
second marble from the bag.
Multiple Events Examples
9. If a coin is flipped twice, what is the probability of it landing heads up both times?
1
1
1 1
1
P(heads 1st time) =
P(heads 2nd time) =
P(heads both times) = * =
2
2
2 2
4
3
1
10. S and T are mutually exclusive events. Find P(S or T) when P(S) = and P(T) = .
5
3
3 1
9
5
14
P(S or T) = + =
+ =
5 3 15 15 15
11. A standard number cube is tossed. Find the probability of P(4 or even).
1 3 1 3
P(4 or even) = + - =
6 6 6 6
2
Rev B
Probability
Multiple Events Practice
12. Suppose you roll 2 number cubes. What is probability that you will roll an odd number on one cube
and a multiple of 3 on the other cube?
13. S and T are mutually exclusive events. Find P(S or T) when P(S) =
1
6
and P(T) =
.
7
10
14. A standard number cube is tossed. Find the probability of P(greater than 1 or less than 5).
3
Rev B