Suppose there is a bag containing 15 green marbles (G), 15 black marbles (B), 15

Question

Suppose there is a bag containing 15 green marbles (G), 15 black marbles (B), 15 red marbles (R), and 15 violet marbles (V). Someone mixes the marbles thoroughly draws one marble at random, puts the marble back in the bag, mixes the bag thoroughly, and draws another marble at random. Complete parts (a) and (b) below. a. List all possible outcomes of this process. Choose the correct answer below. A. GG, GB, GR. GV. BG, BB, BR. BV. RG, RB, RR, RV. VG, VB. VR, VV B. O C. GG, GB, GR, GV, BB, BR, BV, RR, RV, VV 0 D. GB, GR, GV, BR. BV. RV b. Make the probability distribution showing the probability of drawing 0, 1, and 2 black marbles. Probability Result 0 B 1 B 2 B (Simplify your answers.)

Explanation / Answer

a. Possible outcomes are GG, GB, GR, GV, BG, BB, BR, BV,  RG, RB, RR, RV, RG, VB, VR, VV which is given in A.

b. In each draw, the probability of drawing black marble is 15/60 = 0.25.

The probability of not drawing a black marble = 1 - 0.25 = 0.75.

P(0) = 0.75*0.75 = 0.5625

P(1) = 0.25*0.75 + 0.75*0.25 = 0.3750

P(2) = 0.25*0.25 = 0.0625

Result Probability 0 0.5625 1 0.3750 2 0.0625

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