Solutions
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Question
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?
Option A:
1/4
Option B:
1/3
Option C:
1/2
Option D:
7/12
Option E:
2/3
Difficulty Level
HardSolution
Option C is the correct answer.
Option Analysis
The probability of NOT selecting medium out of 3 sizes = 2/3
The probability of NOT selecting red out of 4 colors = 3/4
Total probability of NOT selecting red and medium = (2/3)*(3/4) = 1/2
Required probability = 1 – 1/2 (this will select at least one of red and medium)
= 1/2
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One thought on “A certain store sells small, medium, and large toy trucks in each of the colors red, blue, green, and yellow…”
Here, it is asked probability of AT LEAST ONE of the TWO features. That implies Probability of getting one of the feature as well as both the features.
So, the correct answer will be 7/12 as solved below:
P(Red but NOT Medium) OR P(Medium but NOT Red) OR P(Both Red and Medium) = (1/4 * 2/3) + (1/3 * 3/4) + (1/3 * 1/4) = 7/12 i.e. Option D.