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# Tiles are labeled with the integers from 1 to 100 inclusive; no number

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Math Expert
Joined: 02 Sep 2009
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Tiles are labeled with the integers from 1 to 100 inclusive; no number  [#permalink]

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03 Jan 2019, 11:13
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Difficulty:

25% (medium)

Question Stats:

74% (01:21) correct 26% (01:32) wrong based on 76 sessions

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Tiles are labeled with the integers from 1 to 100 inclusive; no numbers are repeated. If Alma chooses one tile at random, replaces it in the group, and chooses another tile at random, what is the probability that the product of the two integer values on the tiles is odd?

(A) 1/8
(B) 1/4
(C) 1/3
(D) 1/2
(E) 3/4

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Joined: 26 Dec 2018
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Re: Tiles are labeled with the integers from 1 to 100 inclusive; no number  [#permalink]

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03 Jan 2019, 11:38
Given : Tiles are labeled with the integers from 1 to 100 inclusive; no numbers are repeated. If Alma chooses one tile at random, replaces it in the group, and chooses another tile at random,
Question : what is the probability that the product of the two integer values on the tiles is odd?

Product of two integer values is ODD if both the values are ODD.

Both draws have to be ODD. Probability of drawing an Odd numbered tile = 50 /100
Since the first tile is replaced; the Probability of drawing second Odd numbered tile also = 50 /100

Probability that the product of the two integer values on the tiles is odd = (50/100) * (50/100) = 1/4

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Concentration: Sustainability, Marketing
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Re: Tiles are labeled with the integers from 1 to 100 inclusive; no number  [#permalink]

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06 Jan 2019, 04:54
Bunuel wrote:
Tiles are labeled with the integers from 1 to 100 inclusive; no numbers are repeated. If Alma chooses one tile at random, replaces it in the group, and chooses another tile at random, what is the probability that the product of the two integer values on the tiles is odd?

(A) 1/8
(B) 1/4
(C) 1/3
(D) 1/2
(E) 3/4

even integers = 50 and odd would also be 50

product of two odd integers would only give an odd no
so
50/100 * 50/100 = 1/2 * 1/2 = 1/4
IMO B
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Re: Tiles are labeled with the integers from 1 to 100 inclusive; no number  [#permalink]

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18 Feb 2019, 11:24
Out of 100 consecutive ints, 50 are E and 50 are O.
So there is an equal (1/2) chance to choose even or odd.
Choice 1, O (1/2) * Choice 2, O (1/2) = 1/4 both being odd.

Another way to look at it:
We have 4 cases for choosing 2: EE, OO, EO, OE.
Out of 4, only 1 (OO) gives us an odd product, hence 1/4.

Btw, because there's symmetry since each of the 4 cases contains an equal amount, it's easier to think about it logically. If they had a different chance to choose E or O (e.g. 0-10 would have 6/11 chance to choose E and 5/11 chance to choose O) you'd have to multiply the probabilities.
Re: Tiles are labeled with the integers from 1 to 100 inclusive; no number   [#permalink] 18 Feb 2019, 11:24
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