Probability: Simple and Compound Independent and Dependent Experimental and Theoretical

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Probability Simple and Compound Independent
and DependentExperimental and Theoretical
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Understanding Probability
Probability is a measure of how likely an event
is to occur. The probability of an event
occurring is the ratio of the number of favorable
outcomes to the number of possible outcomes. In a
probability experiment, favorable outcomes are
the outcomes that you are interested in.
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Understanding Probability
Probability will help you decide how often
something is likely to occur, but it will never
help you to know exactly when that event will
happen unless the probability is 0 (it will never
happen) or 1 (it will always happen.) The
probability can be expressed as a fraction, a
decimal, or a percent If the probability of an
event is 0, it is impossible. If the probability
of an event is 1, it is certain.
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The more unlikely an event is, the closer its
probability is to 0. The more likely an event is,
the closer its probability is to 1.
The probability, P, of an event occurring is from
0 to 1. If an event is impossible, its
probability is 0. If an event is certain to
occur, its probability is 1.
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Understanding how to find the probability of
events
The probability of an event is the ratio of the
number of favorable outcomes to the number of
possible outcomes.
P(event)
A simple event in a probability experiment is
determined by the outcome of one trial in the
experiment. The probability of a compound event
is the combination of at least two simple events.
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Understanding how to find the probability of
compound events
One way to find the probability of compound
events is to multiply the probabilities of the
simple events that make up the compound event. If
P(A) represents the probability of event A and
P(B) represents the probability of event B, then
the probability of the compound event (A and B )
can be represented algebraically. P(A and B)
P(A) P(B)
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Example
1. What is the probability of drawing a white
marble from a bag containing 3 red marbles and 1
white marble?
2. What is the probability of tossing head
twice on two fair coins tossed at the same time.
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Understanding the difference between dependent
and independent events
If the outcome of the first event does not affect
the possible outcomes of the second event, the
events are called independent events. If two
events are independent, you can use this formula
to find the probability of both events
occurring. P(A and B) P(A) P(B)
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In a compound event, if the outcome of the first
event affects the possible outcomes of the second
event, the events are called dependent events.
Probability (B given A) means the likelihood that
B will happen when A happens. If two events are
dependent, you can use this formula to find the
probability of both events occurring. P(A and B)
P(A) P(B given A)
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Practice
1. A bag contains 10 tiles numbered 1 through 10.
One tile is drawn from the bag. What is the
probability of drawing an even number? 2. You
are playing Concentration and need a 6 to win.
These cards are the only ones left and they are
face down. What is the probability you will
pick a 6?
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3. A probability experiment consists of rolling a
fair number cube numbered 1 through 6 and then
spinning a spinner with two equally likely
outcomes, red or blue. Find the probability of
rolling a 2 on the number cube and spinning red
on the spinner. 4. A bag contains 6 blue
marbles, 4 red marbles, and 2 green marbles. One
marble is drawn from the bag, and its color is
recorded. Another marble is drawn, and its color
is also recorded. What is the probability of
drawing 2 blue marbles if the first marble is not
returned to the bag before the second marble is
drawn?
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5. A bag contains 10 marbles 3 red, 5 blue, and
2 orange. Wendy draws a marble from the bag,
records the color, and then puts the marble back
in the bag. She repeats this for a total of 100
trials.
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6. A local bookstore surveyed to determine what
type of books its customers prefer. The table
below shows the results of the survey.
Based on the survey, if the bookstore plans to
order 400 new books, about how many drama books
should they order? Show your work.