Transcript Advanced Precalculus Advanced Precalculus Notes 12.3
Advanced Precalculus Advanced Precalculus Notes 12.3 Probability
Probability model: 1. Sample space: set whose elements represent all the possible outcomes of an experiment.
2. The measure of how likely it is that some event will occur; a number expressing the ratio of favorable cases to the whole number of cases possible.
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In a bag of M&Ms, the candies are red, green, blue, brown, yellow, and orange. Therefore, the sample space is: { red, green, blue, brown, yellow, orange} Which of the following are probability models:
Outcome
Red Green Blue Brown Yellow orange
Probability
.3
.15
0 .15
.2
.2
Outcome
Red Green Blue Brown Yellow orange .4
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.3
Probability
.1
.1
.1
Outcome
Red Green Blue Brown Yellow orange .4
.2
.2
Probability
.3
-.3
.2
Outcome
Red Green Blue Brown Yellow orange 0 1 0 0 0
Probability
0
An experiment consists of a rolling a fair die once. Construct a probability model for this experiment. a) List the sample space.
b) List the probability of each outcome.
c) Find the probability of each outcome if only 3 or 4 could occur and 4 is twice as likely as 3.
An experiment consists of tossing a coin. The coin is weighted so that heads (H) is three times as likely to occur as tails (T). Construct a probability model for this experiment.
a) List the sample space.
b) List the probability of each outcome.
P(E) = Number of ways that E can occur Number of all logical possibilities
P
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Calculate the probability that in a 3-child family there are 2 boys and 1 girl. Assume equally likely outcomes.
Consider the experiment of rolling a single fair die. Let E represent the event “roll an odd number,” and let F represent the event “roll a 1 or 2.” a) Write the even E and F.
c) Compute P(E) and P(F).
e) Compute
P
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F
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d) Compute
P
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F
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Addition Rule: =
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P
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) If P(E) = 0.2, P(F) = 0.3, and = 0.1, find the probability of E or B. ie:
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F
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Mutually Exclusive Events:
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P
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P
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) If P(E) = 0.4, and P(F) = 0.25, and E and F are mutually exclusive, find
P
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F
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Computing Probabilities of Complementary Events:
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) On the local news the weather reporter stated that the probability of rain tomorrow is 40%. What is the probability that it will not rain?
What is the probability that in a group of 10 people at least 2 people have the same birthday? Assume that there are 365 days in a year.