A bag contains 10 red marbles and 5 blue marbles. You randomly select 3 marbles from the bag. What is the probability that all 3 marbles are blue when (a) you replace each marble before selecting the next one and (b) you do not replace each marble before selecting the next one?

(a) 1/3 (b) 1/3
(a) 1/27 (b) 1/3
(a) 1/27 (b) 2191
(a) 1/3 (b) 2/91

A.) With replacement = 1/27

B.) Without replacement = 2/91

Explanation:

Given the following :

Red marbles = 10

Blue marbles = 5

Probability that all 3 marbles are blue;

A.) With replacement :

Total no marbles = 10 + 5 = 15

P(First pick equals blue) = 5/15 = 1/3

P( second pick equals blue) = 5/15 = 1/3

P( third pick equals blue) = 5/15 = 1/3

P(blue blue blue) = (1/3) × (1/3) × (1/3) = 1/9

B.) Without replacement :

P(First pick equals blue) = 5/15 = 1/3

P( second pick equals blue) = 4/14

P( third pick equals blue) = 3/13

P(blue blue blue) = (1/3) × (4/14) × (3/13 )

= 12/546 = 2/91

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