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If the event A is that where the batch is accepted by the inspector, then A
occurs when all ten items selected belong to the set of acceptable quality
units. The number of elements in A is

NA() = 95 ! = C 95
10 !85 ! 10

and the probability for the event A is

×
×
×
C 95 86 × 87 88 89 90
PA = 10 = = . 0 5837
()
×
×
×
C 100 96 × 97 98 99 100
10
In-Class Exercises
Pb. 10.1 A cube whose faces are colored is split into 125 smaller cubes of
equal size.
a. Find the probability that a cube drawn at random from the batch
of randomly mixed smaller cubes will have three colored faces.
b. Find the probability that a cube drawn from this batch will have
two colored faces.
Pb. 10.2 An urn has three blue balls and six red balls. One ball was ran-
domly drawn from the urn and then a second ball, which was blue. What is
the probability that the first ball drawn was blue?
Pb. 10.3 Find the probability that the last two digits of the cube of a random
integer are 1. Solve the problem analytically, and then compare your result to
a numerical experiment that you will conduct and where you compute the
cubes of all numbers from 1 to 1000.
Pb. 10.4 From a lot of n resistors, p are defective. Find the probability that k
resistors out of a sample of m selected at random are found defective.
Pb. 10.5 Three cards are drawn from a deck of cards.
a. Find the probability that these cards are the Ace, the King, and the
Queen of Hearts.
b. Would the answer change if the statement of the problem was “an
Ace, a King, and a Queen”?

Pb. 10.6 Show that:

PA() =−1 PA( )

where A , the complement of A, are all events in S having no element in com-
mon with A.

© 2001 by CRC Press LLC