AMS310.01 PREQUIZ 2
Practice questions for quiz 2.
_____
1.
P(A
∩
B)= 0.2
P(A)=0.5
P(B)= 0.6, P(BA)=
_______
2.
P(BA) =0.5
P(A)=0.6
P(B)=0.8
P(A
∩
B)= ______
_______
3.
Given
S= {1,2,3,4,5,6} the outcomes of the toss of 1 die.
Let A={we get less than 5 dots} and let B={we get an even number of dots}.
Which statement below is correct?
(a)
A and B independent events.
A and B are mutually exclusive events.
(b)
A and B are dependent events. A and B are mutually exclusive event.
(c)
A and B are independent. A and B are not mutually exclusive.
(d) A and B are dependent events. A and B are not mutually exclusive.
____
4. Given
the values below for F(x), the distribution function of X for all values of X for which
f(x)=Pr(X=x)>0.0.
Find Pr(X
≥
2.5 ).
Hint: F(x) = Pr({
X
≤
x}).
x
0
0.5
1.0
1.5
2.0
2.5
3.0
F(x)
0.1
0.2
0.3
0.5
0.9
0.95
1.0
SOLUTIONS :
1.
2/5=0.4
1.
P(A
∩
B)= 0.2
P(A)=
0.5
P(B)= 0.6, P(BA)=
SOLUTION
: P(BA) = P(A
∩
B)/P(A) = 0.2/0.5 =
0.4
2. 0.30___
2.
P(BA) =
0.5
P(A)=0.6
P(B)=0.8
P(A
∩
B)= ______
SOLUTION
:
P(A
∩
B)= P(AB)
x
P(B) = P(BA)
x
P(A).
Since we are given P(BA) =0.5 and not given
P(AB) we calculate
P(A
∩
B) =
P(BA)P(A) = 0.5 x 0.6 = 0.30.
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 Fall '03
 Mendell
 Toss, mutually exclusive event

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