Probability Assignment
1.

2.b) What is the probability that Toronto wins the series in four games?
3.
i)
Binomial Distribution
The number of trials n is fixed.
Each trial is independent.
Each trial represents one of two outcomes (“success”/”failure”).
The probability of “success” p is the same for each outcome.
The variables of significance are the probabilities of different numbers of
successes.
Geometric Distribution
The number of trials n is not fixed.
Each trial is independent.
Each trial represents one of two outcomes (“success” or “failure”).

The probability of "success" p is the same for each outcome.
The variable of significance is the number of trials required to obtain the first
success.
Hypergeometric Distribution
The number of trials n relies on picking a fixed number k from a larger total n.
Each trial is dependent, as selections are not replaced.
Each trial represents one of two outcomes.
The probability of “success” p is dependent on the previous trials
The variables of interest are the probabilities of our sample containing certain
numbers of the type we are interested in.
ii)
Binomial Distribution
The probability distribution of the number of successes in the sequence of a fixed
number of trials that have two outcomes is modeled by the following formula:
Where:
n
represents the total number of fixed trials.
x
represents the number of successes.
p
represents the probability of success.
To have an
x
number of successes, we must also have an
n-x
number of failures in
n
trials. Also, to have a probability of success,
p,
we must have a
1-p
probability of failure.
Therefore the probability of obtaining a certain sequence of an
x
number of successes
and
n-x
failures can be justified as
p
x
x
(1-p)
(n-x)
. Furthermore, in a sequence of
n
trials,
an
x
number of successes may occur in
n
C
x
ways. This gives the general formula:
n
C
x
x
p
x
x
(1-p)
(n-x)
.

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- Fall '12
- jp
- Probability, Probability theory, Binomial distribution, Geometric distribution, Hypergeometric Distribution