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then:

 n 
P I A k = P A( n )
 k=1 

Pb. 10.10 Find the probability that a positive integer randomly selected will
be non-divisible by:
a. 2 and 3.
b. 2 or 3.
Pb. 10.11 Show that the expression for Eq. (10.36) simplifies to:

n
n
n
PA( ∪ A ∪…∪ A ) = C P A( ) − C PA( ∩ A ) + C PA( ∩ A ∩ A ) −
1 2 n 1 1 2 1 2 3 1 2 3
−
…+ ( 1− ) n 1 PA( ∩ A ∩…∩ A )
1 2 n
when the probability for the intersection of any number of events is indepen-
dent of the indices.
Pb. 10.12 A filing stack has n drawers, and a secretary randomly files m-let-
ters in these drawers.
a. Assuming that m > n, find the probability that there will be at least
one letter in each drawer.
b. Plot this probability for n = 12, and 15 ≤ m ≤ 50.
th
(Hint: Take the event A to mean that no letter is filed in the j drawer and
j
use the result of Pb. 10.11.)

10.4 Conditional Probability

The conditional probability of an event A assuming C and denoted by PAC( )
is, by definition, the ratio:

PA ∩ C)
(
PAC) = (10.37)
(
PC ()
Example 10.7
Considering the events E, O, B, C as defined in Section 10.2 and the above def-
inition for conditional probability, find the probability that the number of
spots showing on the die is even, assuming that it is equal to or greater than 3.

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