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# If x is to be chosen at random from the set {1,2,3,4} and y

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If x is to be chosen at random from the set {1,2,3,4} and y [#permalink]  04 Jan 2004, 14:16
If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {5,6,7}, what is the probability that xy will be even?
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Picking X (1,2,3,4)

Picking Y (5,6,7)

ExE=E
OxE=E
OxO=O

Picking 1=1/4
Then picking 6from next set= 1/3
Thus 1/12

Picking 2=1/4
then picking any from the next set (3/3)
Thus, 1/4

Picking 3 =1/4
then picking 6=1/3
Thus 1/12

Picking 4 = 1/4
then picking any number from next set (3/3)
Thus, 1/4

2/12 + 2/4 = 2/3
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The probability that xy will be odd is 4/12 ....4-(odd*odd -- 1*5,1*7, 3*5,3*7)
12 is the number of total results...4 x 3...

=> 8/12= 2/3 - the probability that xy will be even
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O * O = O
probability of chosing O from first set is 2/4 = 1/2
probability of chosing O from sec set is 2/3
probability of chosing odd mutiple = 1/2 * 2/3 = 1/3

probability of choosing even multiple = 1-1/3 = 2/3
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