Two identical boxes have chips in them. Box I has 4 blue chips and 2 red chips. Box II has 2 blue chips and 6 red chips. A box is randomly selected, and one chip is randomly drawn.
a) What is the probability of drawing a red chip?
b) Given that Box I was chosen, what is the probability of drawing a red chip?
c) Based on your answers in parts a & b, are the events “drawing 1 red chip” and “choosing Box I” dependent or independent? Justify your answer.
Solution:
Given:
Box I: 4 blue chips and 2 red chips. Total = 6 chips
Box II : 2 blue chips and 6 red chips. Total = 8 chips
A box is randomly selected, and one chip is randomly drawn.
Thus
P(Box I )= 0.5 and P(Box II)=0.5 ( since both box has same chance of selection)
Let BI =Box I and BII = Box II
then
P(BI) = 0.5 and P(BII) = 0.5
Part a) What is the probability of drawing a red chip?
P(Red) =...........?
Let R = Red chip
thus we have to find P(R) = .........?
Part b) Given that Box I was chosen, what is the probability of drawing a red chip?
P(R|BI) =.............?
Part c)
Since
Thus the events “drawing 1 red chip” and “choosing Box I” dependent.
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