St. John’s University
03/23/08
Department of Mathematics and Computer Science
Course MTH 1210
Homework #2 (answers)
PROBLEMS INVOLVING CONDITIONAL PROBABILITY
#1.
Women Joggers
. In a certain area, 15% of the population are joggers and 40% of the
joggers are women. If 55% of those who do
not
jog are women, find the probabilities that
an individual from that community fits the following descriptions.
(
a)
A woman jogger
(
b
) Not a jogger
(
c
)
A woman
Event
A
: an individual is a jogger;
P(A) = 0.15
Event
Ā
: an individual is
not
a jogger (the event
Ā
is complementary to
A
).
Event
B
: an individual is a woman
.
Event
BA
: an individual is a woman, given an individual is a jogger;
P(BA) = 0.4
.
Event
BĀ
: an individual is a woman, given an individual is
not
a jogger;
P(BĀ) = 0.55
.
(a)
A woman jogger
: P(B∩A) = P(A∩B) = P(A)*P(BA) =
0.15*0.4
= .06
[see (5.4a,b)]
(b)
an individual is
not
a jogger:
P(Ā) = 1 – P(A) = .85
(c)
A woman:
P(B) =
P(B∩A)
+ P(B∩Ā)
[see (5.6)]
P(B∩Ā) = P(Ā)*P(BĀ) =
0.85*0.55
= 0.4675
Thus,
P(B) =
P(B∩A)
+ P(B∩Ā) =
0.06 + 0.4675
= 0.5275
#2.
Color blindness
. The table below shows relative frequencies for
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 Spring '05
 Kzaer
 Conditional Probability, Probability, Probability theory, Probability space, jogger

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