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

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If x is to be chosen at random from the set {1,2,3}, y is to [#permalink]  29 Jul 2020, 11:02
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Question Stats:

20% (02:52) correct 79% (01:08) wrong based on 24 sessions
If x is to be chosen at random from the set {1,2,3}, y is to be chosen at random from the set {4,5,6}, and z is to be chosen at random from the set {7,8,9,10}, what is the probability that xyz will be even?

A. 1/9

B. 1/2

C. 2/3

D. 7/9

E. 8/9

Kudos for the right answer and explanation
[Reveal] Spoiler: OA

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Re: If x is to be chosen at random from the set {1,2,3}, y is to [#permalink]  29 Jul 2020, 11:22
Expert's post
Carcass wrote:
If x is to be chosen at random from the set {1,2,3}, y is to be chosen at random from the set {4,5,6}, and z is to be chosen at random from the set {7,8,9,10}, what is the probability that xyz will be even?

A. 1/9

B. 1/2

C. 2/3

D. 7/9

E. 8/9

Kudos for the right answer and explanation

One approach is to recognize that P(xyz is even) = 1 - P(xyz is NOT even)
In other words, P(xyz is even) = 1 - P(xyz is ODD)

Aside: This is a useful approach since there's only one way that xyz can be odd. x, y and z must ALL be odd for their product to be odd.
Conversely, there are many different ways for xyz to be even.

P(xyz is odd) = P(x is odd AND y is odd AND z is odd)
= P(x is odd) x P(y is odd) x P(z is odd)
= 2/3 x 1/3 x 2/4
= 1/9

So, P(xy is even) = 1 - 1/9
= 8/9

Cheers,
Brent
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Kudos [?]: 3178 [0], given: 11677

Re: If x is to be chosen at random from the set {1,2,3}, y is to [#permalink]  29 Jul 2020, 11:25
Expert's post
Great explanation
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Re: If x is to be chosen at random from the set {1,2,3}, y is to   [#permalink] 29 Jul 2020, 11:25
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