St. John’s University
Department of Mathematics and Computer Science
Course MTH 1210
Homework #1 (NONCHECKABLE)
Feb 10’07
PROBLEMS INVOLVING CONDITIONAL PROBABILITY
#1.
Suppose that for some activity the probabilities of certain events A and B are as follows:
P(A) = 0.3,
P(B) = 0.4
,
and
P(A∩B) = P(A
and
B) = 0.12
(a) What is
P(AB)
?
(b) What is
P(BA)
?
(c) Are the events
A
and
B
independent?
[ANS
:
(a) 0.3;
(b) 0.4 ;
(c) YES]
#2.
Let
A
and
B
be independent events with probabilities
P(A) = ¼
and
P(B) = 1/5
. Find the
probabilities
P(A∩B)
and
P(A
U
B) .
[ANS: 1/20;
2/5]
#3.
Determine whether or not each of the following pairs of events is independent.
(a)
rolling a pair of dice and observing a “2” on the first die and a “2” on the second die;
(b)
drawing a “heart” from a regular deck of a playing cards and then drawing
another “heart” from the same deck without replacing the first card;
(c)
same as (b) except the first card is returned to the deck before the second drawing;
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 Spring '05
 Kzaer
 Conditional Probability, Probability, Probability theory, Playing card, Card game

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