Let S be a sample space and E and F be events associated with S . Suppose that Pr ( E ) = .6 , Pr ( F ) = .3 , and Pr ( E ∩ F ) = .2 . Calculate a. Pr ( E | F ) b. Pr ( F | E ) c. Pr ( E | F ′ ) d. Pr ( E ′ | F ′ ) .
Let S be a sample space and E and F be events associated with S . Suppose that Pr ( E ) = .6 , Pr ( F ) = .3 , and Pr ( E ∩ F ) = .2 . Calculate a. Pr ( E | F ) b. Pr ( F | E ) c. Pr ( E | F ′ ) d. Pr ( E ′ | F ′ ) .
Solution Summary: The author calculates the value of Pr(E|F) if the sample space is S and the events are E and F.
Let S be a sample space and E and F be events associated with S. Suppose that
Pr
(
E
)
=
.6
,
Pr
(
F
)
=
.3
,
and
Pr
(
E
∩
F
)
=
.2
. Calculate
a.
Pr
(
E
|
F
)
b.
Pr
(
F
|
E
)
c.
Pr
(
E
|
F
′
)
d.
Pr
(
E
′
|
F
′
)
.
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
A research team consists of 4 senior researchers and 10 research assistants. The team needs to select 2 senior researchers and 2 research assistants to attend a conference. How many different ways can the group being sent to the conference be formed?
There are 25 different varieties of flowering plants found in a natural habitat you are studying. You are asked to randomly select 5 of these flowering plant varieties to bring back to your laboratory for further study.
How many different combinations of are possible? That is, how many possible 5 plant subgroups can be formed out of the 25 total plants found?
A person is tossing a fair, two-sided coin three times and recording the results (either a Heads, H, or a Tails, T). Let E be the event that exactly two heads are tossed.
Which of the following sets represent the event E?
Group of answer choices
{HHT, HTH, THH}
{HHT, THH}
{HHH, HHT, HTH, THH, TTT, TTH, THT, HTT}
{HH}
Chapter 6 Solutions
Finite Mathematics & Its Applications (12th Edition)
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