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SOLUTION: We first think about what it is that we need to know. Per the question asked, the
event is that the first and second cards drawn are both Cori‟s.
This event occurs when the 2 cards drawn both come out of the 7 he has put in thus far. Since the
order in which his two cards are drawn don‟t matter (as the prize is the same), we would like to
know the value of
The sample space is simply the total number of outcomes. Two cards will be drawn from the
stack of 40, and since order doesn‟t matter
Thus, the probability of this event is
( )
There is about a 3% chance that both of the cards drawn are Cori‟s.
Example 3: Probability is often used in police investigations to help
determine probable cause. Suppose that in a gang-related report it was
stated that three gang members were spotted. In an interrogation room,
20 gang members are suspects, three of whom are certain to have
committed the crime. A detective has a suspicion that the three came
from a gang of which 5 of its members are present. Just by chance,
how likely is it that the three members came from the gang he believes to be behind the
crime Does this give him what you might consider “probable cause” to pursue the group
SOLUTION: The event is that the three criminals come from a group of five particular gang
members. There are
The total number of way three-criminal groups that can be formed out of the suspects is
This means,
Statistics for Decision-Making in Business © Milos Podmanik Page 126