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Math 166, Fall 2015, Robert
Williams
1.4- Basics of Probability
We cal S a uniform sample space if S is a sample space whose individual
elementary events are equally likely to occur.
Probability of an Event in a Uniform Sample Space: If S is a finite
uniform sample space and E is an event, then the probability of E, denoted
P (E), is
P (E) =
Example 1 Suppose I roll a fair die. Find each of the following:
1. the sample space for the experiment
2. the probability that the die shows a prime number
3. the probability that the die shows a number greater than 8
4. the probability that the die shows a positive number
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Math 166, Fall 2015, Robert
Williams
Example 2 I flip three coins and record whether heads or tails shows; order is
important. Find the probability of the following events:
1. all three coins have the same outcome
2. at least two coins come up as heads
3. exactly one coin comes up as tails
Example 3 A card is drawn from a standard deck of 52 cards. Determine the
probability of each of the following:
1. A 2 is drawn
2. A face card is drawn
3. A club is drawn
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Math 166, Fall 2015, Robert
Williams
Empirical probability is a practical estimate of the probability of an event
occuring. We find empirical probability by
.
A probability distribution table is a table where one row (or column) describes the events that take place and another row (or column) gives the probability of each event occuring.
Example 4 A bottled water company sends their water out in packages of 6
bottles each. After 10, 000 packages are sent to quality control, the following
data is gathered:
Number Defective
0
1
2
3 or more
Packages
8, 921
606
248
125
Using this data, find the empirical probability of purchasing a package of water
with no defects. Find the (empirical) probability of purchasing a package of
water with more than one defective bottle.
Example 5 An experiment is performed where a card is drawn from a deck
of playing cards, it is replaced, shuffled, and then a new card is drawn. The
color of both cards are recorded. Write the probability distribution table for this
experiment.
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Math 166, Fall 2015, Robert
Williams
Example 6 A gambler is curious whether or not his die is fair. He decides to
set up an experiment by rolling his die 100, 000 times and records the outcome
of each trial.
Outcome
1
2
3
4
5
6
Number Observed
16, 832
16, 405
16, 458
16, 763
16, 854
16, 688
Make a probability distribution table for the empirical probability of rolling the
die in question.
Example 7 After the race from one endzone to the other in Kyle Field, the
times of all the participants are recorded. It is discovered that 18 people finished
in less than 10 seconds, 29 people took at least 10 seconds but no more than 15,
40 people took longer than 15 seconds but no more than 20, and 23 people took
more than 20 seconds. Organize this information in a probability distribution
table.
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