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Transcript
```Chapter 7: Probability
Lesson 1: Basic Principles of
Probability
Mrs. Parziale
Vocabulary
• Experiment: a situation that has several
possible results
• Outcomes: results of an experiment
• Sample space: the set of all possible outcomes
• Event: subset of the sample space
• Relative Frequency: comes from conducting an
experiment – is your results from a simulation.
In contrast, probability uses information to
predict future events.
More Terms
• Probability of an event: a number from 0 to 1 that
measures its likelihood.
Notation:
N(E) = the number of elements in a set E
S = sample space
P(E) = the probability that E occurs
Assuming each outcome in S is equally likely
N
(
E
)
# of Outcomes In Event
Formula: P(E) =

# of Outcomes In Sample Space
S
Theorem: Basic Properties of
Probability:
• If S = sample space and P(E) be the probability
of event E, then
• (i) 0  P ( E )  1
• (ii) If E = S, then P(E) = 1
• (iii) If E = {} (empty set), then P(E) = 0.
Example 1:
Toss a fair coin 2 times. Find the probability of
• Sample space: S = { HH, TH, HT, TT } (S = 4)
• N(E) = # of outcomes = 1 (HH)
P(2 heads) = N ( E )  1
S
4
Example 2:
Toss a fair coin 3 times. Find the probability of
Sample space:
S=
Event:
• N(E) (# of outcomes) =
• P(E) =
Example 3:
Roll two die. Take the sum of the numbers
on top.
(a) Event: sum of 10
P(E) =
(b) Event: sum less than 5
P(E) =
(c) Event: sum is less than 50 P(E) =
(d) Event: sum is equal to 1
P(E) =
(e) What sum has the highest probability of occurring?
Example 4:
A researcher is studying the number of boys and girls in families with three
children. Assume that the birth of a boy or a girl is equally likely.
a. Find the probability that a family of three children has exactly one boy.
First identify the sample space.
b. Find the probability that a family of three children has exactly two girls.
Example 5:
Students were testing the theoretical probability of
getting heads or tails when tossing a coin. While
performing an experiment of 2500 tosses, heads
came up 2466 times.
a. What is the probability that the 2501st coin