299 / 762
Chapter 7: Probability
299
Solution:
Let
L
be the event that a student owns a laptop lease from their
university. Let
A
be the event that a student owns a smart phone. Thus,
based on the given information,
P
(
L
) = 83/100 = 0.83 and
P
(
A
|
L
) = 0.62.
We need to compute
P
(
L
A
). From the multiplication rule,
P
(
L
A
) =
P
(
L
)×
P
(
A
|
L
). Thus,
P
(
L
A
) = 0.83×0.62 = 0.5146.
Section Review
7-11 Independence
Independence illustrates a special relationship between events. If having
knowledge of one event does not affect the probability of the occurrence of
another event, then these two events are said to be
independent
. For
example, if
P
(
A
|
B
) = 0.35, and
P
(
A
) = 0.35, then having information about
the event
B
does not affect the probability of the event
A
occurring.
Definition: Independence in Probability
Two events are independent if the occurrence of one does not alter the
probability of the occurrence the other.
So if two events
A
and
B
are independent, then symbolically, we can
express as:
e-Self Review