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Spain Mathematical Olympiad
1981 Spain Mathematical Olympiad
7
7
Part of
1981 Spain Mathematical Olympiad
Problems
(1)
4 machines proude balls at factory, percentages
Source: Spanish Mathematical Olympiad 1981 P7
12/23/2022
In a tennis ball factory there are
4
4
4
machines
m
1
,
m
2
,
m
3
,
m
4
m_1 , m_2 , m_3 , m_4
m
1
,
m
2
,
m
3
,
m
4
, which produce, respectively,
10
%
10\%
10%
,
20
%
20\%
20%
,
30
%
30\%
30%
and
40
%
40\%
40%
of the balls that come out of the factory. The machine
m
1
m_1
m
1
introduces defects in
1
%
1\%
1%
of the balls it manufactures, the machine
m
2
m_2
m
2
in
2
%
2\%
2%
,
m
3
m_3
m
3
in
4
%
4\%
4%
and
m
4
m_4
m
4
in
15
%
15\%
15%
. Of the balls manufactured In one day, one is chosen at random and it turns out to be defective. What is the probability that Has this ball been made by the machine
m
3
m_3
m
3
?
combinatorics
probability