Download Unit-1-Probability

Elementary Statistics
Triola, Elementary Statistics 11/e
Unit 1 Probability Basics
First, some terminology. An event is any collection of results or outcomes of a procedure. For example,
let’s say you flip a coin. Getting a heads or getting a tails would be an event. A sample space is the set
of all possible events. For example, if we use the letter H to represent the event of getting a head, and T
to represent the event getting a tail, then the sample space of a single toss would be {H,T}. If we now
tossed the coin two times, then one possible event would be HH, i.e. heads on the first toss and heads
on the second toss.
Question #1
What would be the sample space of possible events when tossing a coin twice? Use set notation.
Definition of probability.
The probability of an event is the ratio of how many different ways the event can occur to the size of the
sample space. For example, when you flip a coin, there is only one way to get a heads. The size of the
sample space is two, so the ratio is 1 to 2 or ½ or 0.5. We write this as
𝑃(𝐻) =
1
= 0.5
2
Now think of flipping a coin twice. Single events look like {HH} or {HT} where the first letter is the result
of the first flip, and the second letter is the result of the second flip.
Question #2
a. What is the size of the sample space when tossing a coin two times?
b. What is the total number of different ways you can toss a coin twice and get two heads in a row?
c. What is the probability of getting two heads in a row?
The probability of an event that is certain to happen is 1. When you flip a coin, the probability of getting
a heads or a tails is 1 because one or the other must happen. The probability of an event that cannot
possibly happen is 0. When you flip a coin you must get a heads or a tails (we’ll ignore the case of the
coin landing on its rim). Therefore, the probability of getting neither a heads nor a tails is zero. From
this we can conclude that probability is a non-negative number between zero and one.
𝟎≤𝒑≤𝟏
This is the end of Unit 1.
Turn now to your MyMathLab homework to get more
practice with these concepts.
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