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What is the probability that x chosen from S and y chosen from T will

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What is the probability that x chosen from S and y chosen from T will [#permalink]

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New post 27 Sep 2010, 08:48
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S = {1, 2, 3}

T = {4, 5, 6, 7}

What is the probability that x chosen from S and y chosen from T will result x*y = even

A. 1/3

B. 2/3

C. 1/2

D. 5/6

E. 1/6
[Reveal] Spoiler: OA

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Re: What is the probability that x chosen from S and y chosen from T will [#permalink]

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New post 27 Sep 2010, 08:59
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rxs0005 wrote:
S = { 1,2,3,}

T = { 4,5,6,7 }

what is the probability that x chosen from S and y chosen from T will result x*y = even

1/3

2/3

1/2

5/6

1/6


The product of two integers to be even either one (or both) must be even.

So we need probability of choosing even from S OR even from T.

NOTE: Probability of A OR B.
If Events A and B are independent, the probability that either Event A or Event B occurs is:
P(A or B) = P(A) + P(B) - P(A and B) = P(A) + P(B) - P(A)*P(B)

When we say "A or B occurs" we include three possibilities:
A occurs and B does not occur;
B occurs and A does not occur;
Both A and B occur.

So as \(P(S_{even})=\frac{1}{3}\) and \(P(T_{even})=\frac{2}{4}=\frac{1}{2}\) then \(P(S_{even} \ or \ T_{even})=\frac{1}{3}+\frac{1}{2}-\frac{1}{3}*\frac{1}{2}=\frac{2}{3}\).

OR there are 12 pairs possible and out them 8 have either one or both numbers even, so \(P=\frac{8}{12}=\frac{2}{3}\).

Answer: B.
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Re: What is the probability that x chosen from S and y chosen from T will [#permalink]

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New post 27 Sep 2010, 23:12
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rxs0005 wrote:
S = { 1,2,3,}

T = { 4,5,6,7 }

what is the probability that x chosen from S and y chosen from T will result x*y = even

1/3

2/3

1/2

5/6

1/6


p: the probability that x*y is even, then p=1-p(x*y is odd)

p(x*y odd)=p(x odd)*p(y odd)=2/3*2/4=1/3

And p=1-1/3=2/3

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Re: What is the probability that x chosen from S and y chosen from T will [#permalink]

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New post 28 Nov 2017, 08:28
For S=1 and T=4,6. So number of products that are even =2. On the same lines for S=2, we have 4 and for 3 we have 2. So total 8.

8/12 -> 2/3

B

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Re: What is the probability that x chosen from S and y chosen from T will [#permalink]

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New post 28 Nov 2017, 09:28
I did it in a different way.

Is that correct or I accidentally found the correct answer?

Considering that:

S = { 1,2,3,}

T = { 4,5,6,7 }

The propability that S is 1, 2 or 3 = 1/3

If s = 1, we will have an even number if T = 4 or 6, so we have

1/3 * 1/2 = 1/6

If S = 2, any T number will result in an even number, so:

1/3 * 1 = 1/3

If S = 3, we will have an even number if T = 4 or 6, so:

1/3 * 1/2 = 1/6

Then I added all results and found

1/6 + 1/3 + 1/6 = 4/6 = 2/3

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Re: What is the probability that x chosen from S and y chosen from T will   [#permalink] 28 Nov 2017, 09:28
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