I have a question

[Ozlemg]

A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 90 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?

[A] 3/16,000
1/8,100
[C] 3/1,600
[D] 1/90
[E] 2/45

The point where I am confused is why dont we add the violas and cellos to find out the total outcome but multiply them?

OA A

[cans]

# of pairs from same tree=90
total = Select 1 from cello and 1 from viola = 800*600 = 480000
Thus probability = 90/480000 = 3/16,000
IMO A
We need to select one pair(i.e. one cello and one viola)
If we add them, we will get either one cello or one viola not both.

[jainnikhil02]

thanks cans..


Nice question...

[smackmartine]

IMO A

In questions related to pairs, two scenarios can happen:

1) If the selection is done from single group , probability of 1st selection is always 1(if only 1 item is selected).

2) If selection is done from two separate groups (As in this problem)

total pairs are 90

So ,the probability of the two instruments which are made with wood from the same tree is

=(90/800)*(1/600) or (90/600)* (1/800) (order of selection doesn't matter & second selection can be done only in 1 way because the second item must match with 1st item)

=3/16000

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same as OG question!!! OA B