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

Question

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

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

UB001 · Answer

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

Answer Option B is Correct

Archit3110 · Answer

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

energetics · Answer

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.

merajul · Answer

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

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

The odd numbers are as follows - 1,3,5,7,9...99 ; Total Odd Nos. =50.

Now, 1st randomly chosen tile is  replaced in the group  and 2nd tile is randomly chosen from the group. So, each of the number has possibilities = 50
So no of possibilities = 50^2 =2500

Total Integers = 100. Number of Possibilities for the product of 2 integers = 100^2 =10000

Thus P(A) = 2500/10000 = 1/4 (Ans -B)

ScottTargetTestPrep · Answer

In order for the product of the two chosen integers to be odd, both integers must be odd. Since the probability of selecting an odd number is 1/2, the probability of selecting two odd numbers in succession with replacement (thus yielding an odd product) is 1/2 x 1/2 = 1/4.

Answer: B

tam87 · Answer

Most of the solutions have explained the event method...so let me try the longer non-event method.
As choices are made with replacement,
p(getting odd) = 50/100 = 1/2
p( getting even) = 50/100 = 1/2

Now, we can get even in 3 ways = e x o OR o x e OR e x e
P(getting even product) = 1/2 x 1/2 + 1/2 x 1/2 + 1/2 x 1/2 = 3/4
Hence, p(odd product) = 1 - 3/4 = 1/4

Posted from my mobile device

ammoreloaded · Answer

Since result is a product of two numbers and odd, numbers are odd and composite prime. List of composite odd nos : 9,15,21,25,27,33,35,39,45,49,51,55,57,63,65,69,75,77,81,85,87,91,93,95,99

P(A) = 25/100 = 1/4

Just another approach that came to mind. This seems time consuming but remembering first 100 prime nos will save a lot of time.

bumpbot · Answer

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

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