Difference between revisions of "1995 AHSME Problems/Problem 20"
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== Problem == | == Problem == | ||
If <math>a,b</math> and <math>c</math> are three (not necessarily different) numbers chosen randomly and with replacement from the set <math>\{1,2,3,4,5 \}</math>, the probability that <math>ab + c</math> is even is | If <math>a,b</math> and <math>c</math> are three (not necessarily different) numbers chosen randomly and with replacement from the set <math>\{1,2,3,4,5 \}</math>, the probability that <math>ab + c</math> is even is |
Revision as of 10:31, 8 January 2008
Problem
If and
are three (not necessarily different) numbers chosen randomly and with replacement from the set
, the probability that
is even is
Solution
The probability of being odd is
, so the probability of
being even is
.
The probability of being odd is
and being even is
.
is even if
and
are both odd, with probability
; or
and
are both even, with probability
. Thus the total probability is
.
See also
1995 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |