Activity 1 Solutions
1 . A and B are independent events. Which of the following must be true? (4 pts)
a.
A and B are mutually exclusive.
b.
A
c
and B
c
are independent.
c.
)
(
).
(
)
(
B
P
A
P
B
A
P
=
∩
d.
None of the above are true
2. A simple random sample is guaranteed to reflect exactly the population
from which it is drawn. (2 pts)
a.
True
b.
False
3. Consider two events, A and B, of a sample space such that P(A) = P(B) = 0.7.
a.
Is it possible that the two events A and B are mutually exclusive?
Why or
why not?( 3 pts )
No. If A and B are mutually exclusive, P(A or B)=P(A)+P(B)=1.4>1 which is
not
possible.
b.
If the events A and B are independent
, what would be the probability that at
least one of the two events will occur, i.e. P(A or B)? (3 pts)
P(A or B)=P(A)+P(B)P(A
∩
B)=P(A)+P(B)P(A)P(B)
=0.7+0.70.7*0.7
=0.91
c.
Do not assume mutually exclusive or independence
.
Suppose that the
probability of the event B occurring, given that event A has occurred, is 0.6 .
What is the probability that at least one of the two events will occur, that is
P(A or B)? (4 pts)
P(A
∩
B)=P(BA)P(A)=0.7*0.6=0.42.
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 Fall '08
 STAFF
 Mutually Exclusive, Probability theory, pts, probability density function, Cumulative distribution function, exclusive or

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