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

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Senior Manager
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Joined: 17 Mar 2014
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Re: A certain store sells small, medium, and large toy trucks i  [#permalink]

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New post 21 Jul 2018, 14:33
Marcab wrote:
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 \(1/2\)
+1C


never thought of table usage for probability . Good strategy.
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Re: A certain store sells small, medium, and large toy trucks i  [#permalink]

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New post 21 Sep 2018, 21:38
Technically the question doesn't specify the # of trucks... only that there is an equal colour/size combo... we are free to make a simple assumption i.e. 3 sizes * 4 colours = 12 trucks

Probability of at least red or medium = probability of a red truck OR probability of a medium truck
P(R) + P(M) - P(RM) ***remember to watch out for double counting the red and medium truck here (trap answer E)
3/12 + 4/12 - 1/12 = 6/12 = 1/2

Answer = C
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Re: A certain store sells small, medium, and large toy trucks i &nbs [#permalink] 21 Sep 2018, 21:38

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