Statistics for Decision- Making in Business - Maricopa Community ...

) : The Arizona Cardinals make it to the playoffs
Subway runs out of whole wheat bread
c) : Dow Jones Industrial reports an enormous loss
Microsoft stocks plummet
d) ( ) ( ) ( )
e) ( ) ( ) ( ) )
f) ( ) ( ) ( ) )
SOLUTION:
a) Dependent; rain likely greatens the likelihood for accidents
b) Independent; these events probably don‟t have any impact on one another
c) Dependent; Microsoft is part of the Dow Jones Industrial and so there is a strong
relationship between the two
d) Independent; we see that the likelihood of does not change given that has occurred
– it is still .75
e) Dependent; the likelihood of does change given that has occurred – it drops to .3
f) If the product of the two given events does equal the probability of and , then the
events are independent, as this would mean that ( ) is .75, which is the same as
( ). We see that , and so we conclude that the events are independent.
Example 3: An aircraft radar system detects 30 aircraft in a 100-mile radius. Of these, 18 are
ally planes, 6 are cargo planes, and 6 are enemy planes. Given that a plane approaching the radar
is ruled out as being an enemy plane, what is the probability that it is a cargo plane
SOLUTION: First off, define:
We want to know,
( ̅)
Since it is not an enemy plane, it must be one of the remaining 24 aircraft. Of those, 6 are cargo
planes, so
( ̅)
Statistics for Decision-Making in Business © Milos Podmanik Page 109