Question

Suppose there is a bag containing 20 red marbles (R), 20 green marbles (G), 20 pink marbles (P), and 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. RR,RG, RP, RV, GG, GP, GV, PP, PV, W

B. RR, RG, RP, RV, GR, GG, GP, GV, PR, PG, PP, PV, VR, VG, VP, W

C. RG, RP, RV, GP, GV, PV

D. R, G, P, V

b. Make the probability distribution showing the probability of drawing​ 0, 1, and 2 green marbles.

Result	Probability
0G
1G
2 G

Answer 1

So here the bag contains 20 red marbles (R) , 20 green marbles (G) , 20 pink marbles (P) and violet marbles (V). here the number of violet marbles is not given So I am taking it as 20.

a. we are selecting 1 marble at a time and putting back to the bag . Possible outcomes are the result of this experiment. Since we are picking 1 marble at a time So the possible outcomes are red or green or pink or violet marble.

possible outcomes = {R,G,P,V} which is option (d)

b. Number of violet marble is not given It should be given So I am taking number of all marbles as 20.

So probability is a numerical value which describes how much likely an event occur. Or it is simply dividing number of favourable outcome by number of total outcomes. In the question total outcome = 20+20+20+20 = 80

So probability of getting 0 green marble is that the drawn marble may be red or pink or violet which is =     

= 3/4 = 0.75

Probability of getting 1 green marble is =      

probability of getting 2 green marble means we should get green and green So wherever 'and ' comes multiply the probability , wherever 'or' comes add probability (keep in mind),

probability of getting 2 green marble = = 0.0625   

Result	Probability
0G	0.75
1G	0.25
2G	0.0625