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Lloyd has a bag of 3 marbles. There is 1 orange marble, 1 green marble, and 1 blue marble.

List 1 List 2 List 3 List 4
O O, O O, O O, O
G O, G O, G O, G
B O, B O, B O, B
G, O G, O G, O
G, B G, B G, B
G, G G, G G, G
B, B B, B B, B
B, G B, G B, G
B, O B, O
G, O
O, B
G, B

Which list gives the sample space for pulling 2 marbles from the bag with replacement?
List 1
List 2
List 3
List 4

1 answer

When pulling 2 marbles from a bag with replacement, each draw is independent, meaning that the same marble can be drawn more than once. Therefore, we need to consider all possible combinations of 2 marbles, with replacement.

The marbles in the bag are:

  • Orange (O)
  • Green (G)
  • Blue (B)

The possible combinations when pulling 2 marbles with replacement are:

  1. O, O
  2. O, G
  3. O, B
  4. G, O
  5. G, G
  6. G, B
  7. B, O
  8. B, G
  9. B, B

Now, let's check which list matches these combinations:

  • List 1 gives: O, O; O, G; O, B; G, O; G, B; G, G; B, B; B, G; B, O; G, O, O
  • List 2 gives: O, O; O, G; O, B; G, O; G, B; G, G; B, B; B, G; B, O
  • List 3 gives: O, O; O, G; O, B; G, O; G, B; G, G; B, B; B, G; B, O
  • List 4 only gives a limited selection of combinations.

Based on the combinations listed, List 2 accurately reflects the complete sample space for pulling 2 marbles from the bag with replacement.

Thus, the answer is List 2.