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# 2 numbers are chosen from 0-9 inclusive, what is the

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CEO
Joined: 15 Aug 2003
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2 numbers are chosen from 0-9 inclusive, what is the  [#permalink]

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15 Sep 2003, 07:44
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2 numbers are chosen from 0-9 inclusive, what is the
probability that its product will be even?

Is it 7/9?

thanks
praetorian

Kudos [?]: 919 [0], given: 781

Senior Manager
Joined: 22 May 2003
Posts: 328

Kudos [?]: 173 [0], given: 0

Location: Uruguay

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15 Sep 2003, 21:11
I get 3/4

Number of posible pairs of numbers=C(10,2)=40

The only way we get an odd by multplying two numbers is if each of those two numbers are odd.
From 0 to 9 we have 5 odds. So the number of odd pairs is C(5,2)=10

So the answer would be 30/40

Kudos [?]: 173 [0], given: 0

CEO
Joined: 15 Aug 2003
Posts: 3454

Kudos [?]: 919 [0], given: 781

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15 Sep 2003, 21:20
MartinMag wrote:
I get 3/4

Number of posible pairs of numbers=C(10,2)=40

The only way we get an odd by multplying two numbers is if each of those two numbers are odd.
From 0 to 9 we have 5 odds. So the number of odd pairs is C(5,2)=10

So the answer would be 30/40

Martin,

The prob. that the first # can be odd is 5/10 and the prob that the second # is 4/9

So the prob that their product is odd = 5/10 * 4/9 = 2/9

so the prob that the product# is even = 1 - 2/9 =7/9

what did i do wrong?

thanks
praetorian

Kudos [?]: 919 [0], given: 781

Senior Manager
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15 Sep 2003, 21:35
yours is correct

My mistake was to use Combinations instead of Arrengements(permutations)

A(10,2)=10*9=90

A(5,2)=20

Answer=70/90=7/9

It's late man

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Intern
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15 Sep 2003, 23:27
hold on fellows. praetorian, you are using the logic that 1 - prob that multiple is odd = prob that multiple is even rt?

thus 1 -( 5/10 X 4/9) = 7/9.

however since the number 0 is included there is a possibility that the multiple will be neither odd nor even. hence the answer cannot be 7/9.

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16 Sep 2003, 00:07

wow. even though i am exremely embarrased i feel thankful that i do know that 0 is even. goes to show how a simple fact like this could have been the end of me.

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16 Sep 2003, 11:44
1. Any number that is a multiple of 2 is even. So 0 is neither even or odd.

2. The probability that the product of 2 nos from 0-9 is even is,
(2,4,6,8) are even numbers, 4/10.

As we need to select only one number to make the product even. The selection of the second number is immaterial, because it could be even or odd.

In the approach where is the answer is 7/9, this is the answer for getting the probability of two even numbers, as 1-P(of getting to 2 even nos.)

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Manager
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16 Sep 2003, 14:14
watchdog wrote:
1. Any number that is a multiple of 2 is even. So 0 is neither even or odd.

2. The probability that the product of 2 nos from 0-9 is even is,
(2,4,6,8) are even numbers, 4/10.

As we need to select only one number to make the product even. The selection of the second number is immaterial, because it could be even or odd.

In the approach where is the answer is 7/9, this is the answer for getting the probability of two even numbers, as 1-P(of getting to 2 even nos.)

0 is even, and is neither positive nor negative.
_________________

Sept 3rd

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16 Sep 2003, 14:14
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# 2 numbers are chosen from 0-9 inclusive, what is the

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