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Set A contains three different positive odd integers and two

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Set A contains three different positive odd integers and two [#permalink] New post 03 Aug 2014, 11:05
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Set A contains three different positive odd integers and two different positive even integers; set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?

(A) 6/25
(B) 2/5
(C) 1/2
(D) 3/5
(E) 19/25
[Reveal] Spoiler: OA
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Re: Set A contains three different positive odd integers and two [#permalink] New post 03 Aug 2014, 11:33
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oss198 wrote:
Set A contains three different positive odd integers and two different positive even integers; set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?

(A) 6/25
(B) 2/5
(C) 1/2
(D) 3/5
(E) 19/25


My approach- probability of product even(P(E)) = 1- probability of product odd(P(O))

Odd product is possible only when an integer picked from both sets is odd, so..

P(O) = (3c1* 2c1)/5c1*5c1
= 6/25
P(E) = 1-6/25 = 19/25.

Hope it helps
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Re: Set A contains three different positive odd integers and two [#permalink] New post 09 Aug 2014, 00:43
oss198 wrote:
Set A contains three different positive odd integers and two different positive even integers; set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?

(A) 6/25
(B) 2/5
(C) 1/2
(D) 3/5
(E) 19/25


Another approach:

P (product of 2 chosen integers is even) = P(E&E) + P(E&O) + P (O&E) = 2/5*3/5 + 2/5*2/5 + 3/5*3/5 = 19/25
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Re: Set A contains three different positive odd integers and two [#permalink] New post 10 Aug 2014, 00:42
Three approaches:
1. Backward (the shortest)
P(product even)=1-P(product odd)=1-P(odd from A)*P(odd from B)=1-3/5*2/5=19/25

2. The previous post
P (product of 2 chosen integers is even) = P(E&E) + P(E&O) + P (O&E) = 2/5*3/5 + 2/5*2/5 + 3/5*3/5 = 19/25

3. Using formula for overlapping sets
P(even from A or even from B)=P(even from A)+P(even from B)-P(even from A and even from B)=2/5+3/5-2/5*3/5=19/25
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Re: Set A contains three different positive odd integers and two   [#permalink] 10 Aug 2014, 00:42
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Set A contains three different positive odd integers and two

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