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Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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100 tiles are labeled with the integers from 1 to 100 inclus [#permalink]
Expert's post 00:00

Question Stats: 86% (01:04) correct 14% (00:47) wrong based on 50 sessions
100 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) $$\frac{1}{8}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{1}{3}$$
(D) $$\frac{1}{2}$$
(E) $$\frac{3}{4}$$
[Reveal] Spoiler: OA

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Sandy
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Moderator  Joined: 07 Jan 2018
Posts: 697
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Re: 100 tiles are labeled with the integers from 1 to 100 inclus [#permalink]
Total number of tiles = 100
Numbering starts with odd and ends with even. i.e from 1 to 100. Therefore there are 50 odd tiles and 50 even tiles.

For product of two number to be odd, both number has to be odd.
Hence number of successful outcome = 50 * 50
Number of possible outcome = 100* 100
Probability = 50*50/100*100 = 1/4

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Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3033 , given: 394

Re: 100 tiles are labeled with the integers from 1 to 100 inclus [#permalink]
Expert's post
Explanation

Use both probability and number properties concepts in order to answer this question.

First, in order for two integers to produce an odd integer, the two starting integers must be odd. An odd times an odd equals an odd. An even times an odd, by contrast, produces an even, as does an even times an even.

Within the set of tiles, there are 50 even numbers (2, 4, 6, …, 100) and 50 odd numbers (1, 3, 5, …,99).

One randomly-chosen tile will have a $$\frac{50}{100}=\frac{1}{2}$$ probability of being even, and a $$\frac{1}{2}$$ probability of being odd.

The probability of choosing an odd tile first is $$\frac{1}{2}$$ and the probability of choosing an odd tile second is also , so the probability of “first odd and second odd” is $$\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$$.
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GRE Instructor Joined: 10 Apr 2015
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Re: 100 tiles are labeled with the integers from 1 to 100 inclus [#permalink]
Expert's post
sandy wrote:
100 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) $$\frac{1}{8}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{1}{3}$$
(D) $$\frac{1}{2}$$
(E) $$\frac{3}{4}$$

There are 100 tiles. 50 tiles are EVEN and 50 tiles are ODD
The only way to get an ODD product is for the 1st tile to be ODD AND the 2nd tile to be ODD

So, P(product is ODD) = P(1st tile is ODD AND the 2nd tile is ODD)
= P(1st tile is ODD) x P(2nd tile is ODD)
= 50/100 x 50/100
= 1/2 x 1/2
= 1/4

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com  Re: 100 tiles are labeled with the integers from 1 to 100 inclus   [#permalink] 10 Aug 2018, 05:12
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