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CCA Math Bonanza
2022 CCA Math Bonanza
T8
T8
Part of
2022 CCA Math Bonanza
Problems
(1)
Set Probability
Source:
4/27/2022
Let n be a set of integers.
S
(
n
)
S(n)
S
(
n
)
is defined as the sum of the elements of n.
T
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
}
T=\{1,2,3,4,5,6,7,8,9\}
T
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
}
and A and B are subsets of T such that A
∪
\cup
∪
B
=
T
B=T
B
=
T
and A
∩
\cap
∩
B
=
∅
B=\varnothing
B
=
∅
. The probability that
S
(
A
)
≥
4
S
(
B
)
S(A)\geq4S(B)
S
(
A
)
≥
4
S
(
B
)
can be expressed as
p
q
\frac{p}{q}
q
p
. Compute
p
+
q
p+q
p
+
q
.2022 CCA Math Bonanza Team Round #8
probability