Replacement in probability : concept

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Sun Jul 24, 2011 12:07 am

1>What is the probability that one of the two integers randomly selected from range 20-29 is prime and the other is a multiple of 3?

[spoiler]{2/10 * 3/10} *2 = .12[/spoiler]

2>A basket contains 13 fruits: 5 apples and 8 pears. What is the probability that 2 fruits drawn from the basket at random will be pears?

[spoiler]8/13*7/12 = 14/39[/spoiler]

Both question above are from gmat club tests. My query is when do we consider that we are talking about replacements ? I mean the answer trap to the second question could have been 8/13*8/13 (if we considered that the fruit is replaced after withdrawal)

In my first question if we considered that the prime is not being put back then the solution would be {2/10 * 3/9} *2

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Source: Beat The GMAT — Problem Solving | Sun Jul 24, 2011 12:07 am

knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Sun Jul 24, 2011 1:02 am

We consider replacement only and only when it is stated or implicitly understood. In the first question we consider it as replacement simply because you picking a number from there does not deplete one number from the pool. But on the other hand if you had the numbers 20-29 written on chits of paper and placed in a bowl and 2 chits were picked out without replacement that would deplete numbers from the bowl. And in the second scenario the answer would be {2/10 * 3/9} *2. This concept is also applied to question 2

In question 2. Thinking outside the scope of mathematics....When a fruit is taken out of a basket the same fruit cannot be picked out of the basket again. You can only select from one of the remaining fruits. So taking a fruit out of the basket reduces the number of possible options by one.

Last edited by knight247 on Sun Jul 24, 2011 3:23 am, edited 1 time in total.

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naveen451: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Sat Jul 16, 2011 11:56 pmFollowed by: 1 member; Location: hyderabad; Thanked: 2 times

by naveen451 » Sun Jul 24, 2011 2:37 am

in first question
{2/10*3/10}*2 is the ans

whatis the need of *2

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Sun Jul 24, 2011 3:08 am

Specific order is not mentioned in the problem. It could be P(Prime)*P(# divisible by3)+P(# divisible by3)*P(Prime). Hence the 2

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