Statistics Examples

Determine if B and A are Independent/Dependent Events
, ,
Two events are independent events when the occurrence of one does not affect the probability of the other. and .
should equal to because the occurrence of should not effect the probability of for independent events and . In this case, .
Find using Bayes's rule.
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Using the Bayes' rule, .
Substitute the given values , , and in Bayes' rule.
Simplify .
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Remove parentheses.
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Multiply by .
Multiply by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
should equal to because the occurrence of should not effect the probability of for independent events and . In this case, .
and , which means that and are independent events.
A and B are independent events
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