Question

5. 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.

Answer 1

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Let a consider drawing of a red chies ut a consider the Box I, which has 4 blue chibs & 2 reaching let. B . .; Box I,. i 21. 1 p (choosing Box I) = 1/4 = P(A) P (Drawing a red chiks) . pl choosing Box I) = { - PCB). PR) :P (RIA) PIA) + PL RIB) P18) (3) 1 (1) . 1927 18 24. by P ( In Box I, drawing a red chiles) : PIRIA). PIA) . .(3).1.1 (1) ? c) Based on my answers in bury (a) & (b) PIRI = 1 1 4 ple from Box I) = 1/2 we know it two events are indpendent then, PERIA) - PCRDi . But here, pl draning I red chits) & P (Drawing 1 red chips from Box I) Then, the events are dependent,