Question

franciscos 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.

Explanation:

Step1: Recall probability concept

Probability of selecting yellow = $\frac{\text{Number of yellow marbles}}{\text{Total number of marbles}}$. To increase the probability, we need to increase the number of yellow marbles or decrease non - yellow marbles.

Step2: Analyze option 1

Adding green marbles increases total marbles without increasing yellow, so probability of yellow decreases.

Step3: Analyze option 2

Adding more yellow marbles increases the numerator while total marbles also increase, but proportionally increases the probability of yellow.

Step4: Analyze option 3

Removing 1 green, 1 black and 2 red marbles decreases non - yellow marbles. So probability of yellow increases.

Step5: Analyze option 4

Adding more black marbles increases total marbles without increasing yellow, so probability of yellow decreases.

Step6: Analyze option 5

Tripling the number of yellow marbles greatly increases the numerator, increasing the probability of yellow.

Answer:

B. Andrew should add more yellow marbles to the bag.
C. Andrew should remove from the bag 1 green, 1 black, and 2 red marbles.
E. Andrew should triple the number of yellow marbles in the bag.