Statistics Assignment #2
1.
P.134, 3.42
a.
Sample points are the most basic outcome of an experiment.
A:{{1,6}, {6,1}, {2,5}, {5,2}, {3,4}, {4,3}}
B: {{1,4}, {2,4}, {3,4}, {4,4}, {5,4}, {6,4}, {4,1}, {4,2}, {4,3}, {4,5}, {4,6}}
The intersection of A and B is the event that occurs if we roll both a 7 and at
least one of the two dice is showing a 4. Therefore the sample points for the
intersection are:
A
∩
B: {{3,4}, {4,3}}
The union of A and B is the event that occurs if we observe a sum of 7, at
least one of the two dice showing a 4 or both on a single throw of the die. The
sample points in the event A
∪
B are those for which A occurs, B occurs, or
both A and B occur. The sample points for the union are:
A
∪
B: {{1,6}, {6,1}, {2,5}, {5,2}, {3,4}, {4,3}, {1,4}, {2,4}, {4,4}, {5,4}, {6,4}, {4,1},
{4,2}, {4,5}, {4,6}}
We know that A :{Observe a sum of 7} and the compliment of A is defined as
the event that occurs when A does not occur. Therefore,
A
c
:{Observe no sum of 7}={{1,1}, {1,2}, {1,3}, {1,4}, {1,5},
{2,1}, {2,2}, {2,3}, {2,4}, {2,6}
{3,1}, {3,2}, {3,3}, {3,5}, {3,6},
{4,1}, {4,2}, {4,4}, {4,5}, {4,6},
{5,1}, {5,3}, {5,4}, {5,5}, {5,6},
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View Full Document{6,2} , {6,3} , {6,4} , {6,5} , {6,6}}
b.
We can assume that all pairs of outcomes have probability 1/36.
Since the event A contains 6 sample points all with probability 1/36 we
reason that the probability of A is the sum of the probabilities of the sample
points in A.
P(A)= 1/36+1/36+1/36+1/36+1/36+1/36
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 Winter '08
 DrJoseCorrea
 Probability, Probability theory, Summation, Sample points

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