Question

Adjusting the Probability
Francisco’s game involves a bag of 3 green, 2 yellow, 4 red, and 3 black marbles. Andrew wants to increase the likelihood of selecting a yellow marble. How can the game be modified to make drawing a yellow marble more likely? Select all that apply.
Andrew should add more green marbles to the bag.
Andrew should add more yellow marbles to the bag.
Andrew should remove from the bag 1 green, 1 black, and 2 red marbles.
Andrew should add more black marbles to the bag.
Andrew should triple the number of yellow marbles in the bag.

Answer 1

Correct choices:
- Andrew should add more yellow marbles to the bag.
- Andrew should remove from the bag 1 green, 1 black, and 2 red marbles.
- Andrew should triple the number of yellow marbles in the bag.

Brief reasoning:
- Initially P(yellow) = 2/12 = 1/6 ≈ 0.1667.
- Adding non-yellow (green or black) increases the total but not the yellow count, so P(yellow) falls.
- Adding yellow increases the yellow numerator, so P(yellow) rises.
- Removing 1 green, 1 black, and 2 red leaves counts 3→2, 2, 4→2, 3→2 so total 8 with 2 yellow ⇒ P = 2/8 = 1/4 > 1/6.
- Tripling yellow gives 6 yellow out of 16 total ⇒ P = 6/16 = 3/8 > 1/6.