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X and Y are two data sets that contain integers as shown the table abo

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Bunuel
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X and Y are two data sets that contain integers as shown the table abo [#permalink] New post   02 Jun 2020, 09:02
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Frequency Distribution of Integers in Data Set X and Data Set Y



X and Y are two data sets that contain integers as shown the table above. What is the probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even?

A. 1/15
B. 13/354
C. 1/5
D. 1/2
E. 4/5

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D
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Re: X and Y are two data sets that contain integers as shown the table abo [#permalink] New post   06 Jun 2020, 05:35
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Bunuel wrote:
Frequency Distribution of Integers in Data Set X and Data Set Y



X and Y are two data sets that contain integers as shown the table above. What is the probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even?

A. 1/15
B. 13/354
C. 1/5
D. 1/2
E. 4/5

Show Spoiler
Attachment:
1.png


Solution:

Notice that set X has 30 numbers, of which 12 are even and 18 are odd. Similarly, set Y has 12 numbers, of which 2 are even and 10 are odd.

P(even product)

= P(odd from X, even from Y) + P(even from X, odd from Y) + P(even from X, even from Y)

= 18/30 x 2/12 + 12/30 x 10/12 + 12/30 x 2/12

= 3/5 x 1/6 + 2/5 x 5/6 + 2/5 x 1/6

= 3/30 + 10/30 + 2/30

= 15/30 = 1/2

Alternate Solution:

We can use the fact that P(even product) = 1 - P(odd product) and that P(odd product) = P(odd from X, odd from Y).

Since X has 30 numbers, of which 12 are even and 18 are odd; P(odd from X) = 18/30 = 3/5. Similarly, since set Y has 12 numbers, of which 2 are even and 10 are odd; P(odd from Y) = 10/12 = 5/6.

So, P(odd product) = 3/5 x 5/6 = 3/6 = 1/2. It follows that P(even product) = 1 - 1/2 = 1/2.

Answer: D
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Re: X and Y are two data sets that contain integers as shown the table abo [#permalink] New post   02 Jun 2020, 09:10
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Bunuel wrote:
Frequency Distribution of Integers in Data Set X and Data Set Y



X and Y are two data sets that contain integers as shown the table above. What is the probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even?

A. 1/15
B. 13/354
C. 1/5
D. 1/2
E. 4/5

Show Spoiler
Attachment:
1.png


Given: X and Y are two data sets that contain integers as shown the table above.

Asked: What is the probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even?

Probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even = 1 - Probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be odd

Probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be odd = \(\frac{18}{30} * \frac{10}{12} = \frac{3}{5} * \frac{5}{6} = \frac{3}{6} = \frac{1}{2 }\)

Probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even = 1 - Probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be odd = \(1 - \frac{1}{2 }= \frac{1}{2}\)

IMO D
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X and Y are two data sets that contain integers as shown the table abo [#permalink] New post   28 Oct 2020, 00:22
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Bunuel wrote:
Frequency Distribution of Integers in Data Set X and Data Set Y



X and Y are two data sets that contain integers as shown the table above. What is the probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even?

A. 1/15
B. 13/354
C. 1/5
D. 1/2
E. 4/5

Show Spoiler
Attachment:
1.png


Set X has 30 elements out of which (3 + 9) = 12 are even and (4 + 6 + 8) = 18 are odd.
Set Y has 12 elements out of which 2 are even and (1 + 2+ 4+ 3) = 10 are odd.

Many ways of doing this:

Method 1: Find the probability of the complement since it is easier.

P(Odd Product) = (18/30) * (10/12) = 1/2
P(Even Product) = 1 - 1/2 = 1/2


Method 2: Use logic of sets to find the even product

P(Even Product) = P(Even from X) + P(Even from Y) - P(Both Even)
P(Even Product) = 12/30 + 2/12 - (12/30)*(2/12) = 1/2


Method 3: Simply calculate the probability

P(Even Product) = P(Even from X but Odd from Y) + P(Odd from X but Even from Y) + P(Even from Both)
P(Even Product) = 12/30 * 10/12 + 2/12 * 18/30 + 12/30 * 2/12 = 1/2
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Re: X and Y are two data sets that contain integers as shown the table abo [#permalink] New post   02 Jun 2020, 12:41
IMO D

Product of two number even when: (Even from box 1 * Odd from box 2) OR (Even from box 1 * Odd from box 2) OR (Even from box 1 * Even from box 2)

We need to find the probability for above cases.

OR We can calculate Probability as 1 - Probability the product will be ODD

Product of two number odd when: ODD * ODD
SIMPLE :)

Probability the product will be ODD = (Ways of selecting ODD number from box 1 * Ways of selecting ODD number from box 2) / (Ways of selecting a number from box 1 * Ways of selecting a number from box 2)

= 18 * 10 / 30 *12 = 1/2

Probability that product will be Even = 1 -1/2 = 1/2
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Re: X and Y are two data sets that contain integers as shown the table abo [#permalink] New post   26 Oct 2020, 11:17
The source of this question is egmat.
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Re: X and Y are two data sets that contain integers as shown the table abo [#permalink] New post   28 Oct 2020, 00:06
Event: Pick Number from Set X and Pick Number from Set Y


there are 3 Scenarios in which we can Draw a Number from Each Set and have an Even Product:


Scenario 1:
Pull ODD from X -----> Probability = 18/30
and
Pull EVEN from Y ------> Probability = 2/12

3/5 * 1/6 = 3/30 or

1/10-----


OR +

Scenario 2:
Pull EVEN from X ------> Probability = 12/30
and
Pull ODD from Y ------> Probability = 10/12

2/5 * 5/6 = 10/30 or

1/3------


OR +


Scenario 3:
Pull EVEN from X ----> 12/30
and
Pull EVEN from Y -----> 2/12

2/5 * 1/6 = 2/30------



adding the Probabilities from the 3 Scenarios:

(1/10) + (1/3) + (2/30) =

(3/30) + (10/30) + (2/30) =

15/30 =


1/2
Answer -D-
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Re: X and Y are two data sets that contain integers as shown the table abo [#permalink]
28 Oct 2020, 00:06
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