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

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Math Expert
Joined: 02 Sep 2009
Posts: 65014
X and Y are two data sets that contain integers as shown the table abo  [#permalink]

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02 Jun 2020, 08:02
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5
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Difficulty:

55% (hard)

Question Stats:

63% (02:20) correct 37% (02:14) wrong based on 43 sessions

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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

Attachment:

1.png [ 12.87 KiB | Viewed 579 times ]

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Re: X and Y are two data sets that contain integers as shown the table abo  [#permalink]

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02 Jun 2020, 08:10
1
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

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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Re: X and Y are two data sets that contain integers as shown the table abo  [#permalink]

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02 Jun 2020, 11:41
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]

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06 Jun 2020, 04:35
1
1
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

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.

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Re: X and Y are two data sets that contain integers as shown the table abo   [#permalink] 06 Jun 2020, 04:35