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probability that the truck

by Needgmat » Thu Sep 29, 2016 8:12 am
A certain store sells small, medium, and large toy trucks in each of the color 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 of 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

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by GMATGuruNY » Thu Sep 29, 2016 8:15 am
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 of 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
To make the situation easier to evaluate, let there be ONE of each size-color combination.
Draw a CHART and put an "X" under any truck that is either red, medium or both:
Image
Of the 12 trucks in the chart, 6 are either red, medium or both.
P(selecting a good truck) = 6/12 = 1/2.

The correct answer is C.
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by DavidG@VeritasPrep » Thu Sep 29, 2016 8:28 am
Needgmat wrote:A certain store sells small, medium, and large toy trucks in each of the color 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 of 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

OAC
We can use our trusty P(x or y) formula. P(x or y) = P(x) + P(y) - P(x and y) In this case, we want P(red or medium).

P(red or medium) = P(red) + P(medium) - P(red and medium)

P(red) = 1/4 (there are 4 colors to choose from)
P(medium) = 1/3 (there are 3 sizes to choose from)
P(red and medium) = (1/4)*(1/3) = 1/12

(red) + P(medium) - P(red and medium) = 1/4 + 1/3 - 1/12 = 6/12 = 1/2. Answer is C
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by DavidG@VeritasPrep » Thu Sep 29, 2016 8:29 am
(And notice the predictable traps in the answer choices. 1/4 and 1/3 are there. And 7/12 is just 1/4 + 1/3.)
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by Matt@VeritasPrep » Thu Sep 29, 2016 6:20 pm
There are three size options and four color options, so

1/(# of size) * 1/(# of colors) = unique combo

Paul is happy with any of these:

Red + Small
Red + Medium
Red + Large
Blue + Medium
Green + Medium
Yellow + Medium

so 6 of the combos will work, giving us 6 * (1/12), or 1/2.
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by Matt@VeritasPrep » Thu Sep 29, 2016 6:22 pm
DavidG@VeritasPrep wrote:(And notice the predictable traps in the answer choices. 1/4 and 1/3 are there. And 7/12 is just 1/4 + 1/3.)
... and this is great advice, watch out for the easy-looking answers in any problem, PS, DS, CR, SC, wherever! I've saved myself from a lot of embarrassing blunders in front of groups just by doing this ("It's obviously D ... but wait, this person is ASKING me how to solve it, so he must've thought it was D too, so something sinister is afoot. Aha! There it is, it's actually B.")
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