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A certain store sells small, medium, and large toy trucks i

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A certain store sells small, medium, and large toy trucks i [#permalink] New post 08 Jan 2013, 04:36
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A certain store sells small, medium, and large toy trucks in each of the colors red, blue, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?

A. 1/4
B. 1/3
C. 1/2
D 7/12
E. 2/3
[Reveal] Spoiler: OA

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Re: A certain store sells small, medium, and large toy trucks i [#permalink] New post 08 Jan 2013, 05:04
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fozzzy wrote:
A certain store sells small, medium, and large toy trucks in each of the colors red, blue green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?

A. 1/4
B. 1/3
C. 1/2
D 7/12
E. 2/3


let there be x number of trucks of all possible color-size combination.
probability that the truck she selects will have at least one of the two features Paul wants can be found by subtracting the probability of selecting a truck that doesn't has either of the property i.e. it is neither red in color nor of medim size from 1.

In the diagram attached, the I crossed off all the desired results i.e. cancelled all the possible combination of red-medium.
# of remaining outcomes= # of blue circles = # of trucks that don't have either of the desired property.

No. of colors=4
no. of sizes=3
Total outcomes=12

Remaining outcomes=6
hence probability that truck is neither red nor of medium size is 6/12.
hence probability that the truck she selects will have at least one of the two features Paul wants will be 1 - 6/12 or 1/2
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probability.png
probability.png [ 9.42 KiB | Viewed 2657 times ]


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Re: A certain store sells small, medium, and large toy trucks i [#permalink] New post 08 Jan 2013, 06:53
Great Explanation! Thanks!
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Re: A certain store sells small, medium, and large toy trucks i [#permalink] New post 08 Jan 2013, 08:05
Assume there are 1 of each giving - 3 sizes x 4 colours = 12 trucks

Since the q is asking for "at least one" (medium truck or red truck) let's calculate probability of selecting neither a red or medium truck and subtract from 1

Therefore - 1 - 6/12 = 1/2
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Re: A certain store sells small, medium, and large toy trucks i [#permalink] New post 08 Jan 2013, 08:22
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The key is to take in account whenever see you the word AT Least is to subtract the other probability from 1

In this case you DO NO want the large and the small size so 2/3AND (means *) the other colors so3/4

From this 1 - 2/3 * 3/4 = 1 - 6/12 = 6/12 = 1/2
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Re: A certain store sells small, medium, and large toy trucks i [#permalink] New post 27 Jan 2013, 04:24
fozzzy wrote:
A certain store sells small, medium, and large toy trucks in each of the colors red, blue green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?

A. 1/4
B. 1/3
C. 1/2
D 7/12
E. 2/3


Please add a comma between blue and green. I mistook it as 1 category!
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Re: A certain store sells small, medium, and large toy trucks i [#permalink] New post 07 Mar 2014, 19:21
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Re: A certain store sells small, medium, and large toy trucks i   [#permalink] 07 Mar 2014, 19:21
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