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HW 1:
Solutions
2.3.
a.
Event A = { SSF, SFS, FSS }
b.
Event B = { SSS, SSF, SFS, FSS }
c.
For Event C, the system must have component 1 working ( S in the first position), then at least one
of
the other two components must work (at least one S in the 2
nd
and 3
rd
positions:
Event C = { SSS,
SSF, SFS }
d.
Event C
= { SFF, FSS, FSF, FFS, FFF }
Event A
C = { SSS, SSF, SFS, FSS }
Event A
C = { SSF, SFS }
Event B
C = { SSS, SSF, SFS, FSS }
Event B
C = { SSS SSF, SFS }
2.13.
a.
awarded either #1 or #2 (or both): P(A
1
A
2
) = P(A
1
) + P(A
2
)  P(A
1
A
2
) = .22 + .25  .11 = .36
b.
awarded neither #1 or #2: P(A
1
A
2
) = P[(A
1
A
2
)
] = 1  P(A
1
A
2
) = 1  .36 = .64
f.
either (neither #1 nor #2) or #3: P[( A
1
A
2
)
A
3
] = P(awarded none) + P(A
3
)
= .47 + .28 = .75
2.22
a. P(A
1
A
2
) = P(A
1
) + P(A
2
)  P(A
1
A
2
) = .4 + .5  .6 = .3
b.
P(A
1
A
2
) = P(A
1
)  P(A
1
A
2
) = .4  .3 = .1
c.
P(exactly one) = P(A
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This note was uploaded on 03/22/2011 for the course STAT 427 taught by Professor Staff during the Spring '08 term at Ohio State.
 Spring '08
 Staff
 Probability

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