Question

each bag below has 6 marbles. austin closes his eyes and picks a marble from each bag.
bag a
bag a has 2 yellow marbles, 2 red marbles, and 2 blue marbles.
picking a yellow marble from bag a is ______.
○ certain
○ likely
○ unlikely
○ impossible
bag b
bag b has 2 red marbles and 4 blue marbles.
picking a yellow marble from bag b is ______.
○ certain
○ likely
○ unlikely
○ impossible
bag c
bag c has 4 yellow marbles, 1 red marble, and 1 blue marble.
picking a yellow marble from bag c is ______.
○ certain
○ likely
○ unlikely
○ impossible

Explanation:

Bag A:

Step1: Analyze Bag A's marbles

Bag A has 2 yellow, 2 red, 2 blue marbles. Total = 6. Yellow marbles: 2. Probability of yellow: $\frac{2}{6}=\frac{1}{3}$. Since it's neither 0 (impossible) nor 1 (certain), and 1/3 is moderate, but among the options, "likely" or "unlikely"? Wait, 2 out of 6: the chance is 1/3. Let's check the options. The options are certain (1), likely (more than 1/2?), unlikely (less than 1/2), impossible (0). 1/3 < 1/2, so it's unlikely? Wait no, wait: Bag A has 2 yellow, 2 red, 2 blue. So picking yellow: 2/6 = 1/3. So it's possible but not likely (likely would be more than 50%), so "unlikely"? Wait no, wait the options: certain (1), likely (probability > 0.5), unlikely (probability < 0.5), impossible (0). So 1/3 is less than 0.5, so "unlikely"? Wait no, wait maybe I miscalculated. Wait Bag A: 2 yellow, 2 red, 2 blue. So total 6. So yellow is 2. So probability 2/6 = 1/3 ≈ 0.33. So it's not certain, not impossible. Likely is when probability is high (more than 0.5), unlikely is low (less than 0.5). So 0.33 is low, so "unlikely"? Wait no, wait the options for Bag A: the choices are certain, likely, unlikely, impossible. Wait maybe I made a mistake. Wait Bag A has yellow marbles (2), so it's possible. The probability is 2/6 = 1/3. So among the options, "unlikely" because it's less than 50%? Wait no, maybe the question is about the likelihood. Let's re-examine:

Bag A: 2 yellow, 2 red, 2 blue. So picking yellow: possible, but not certain, not impossible. The chance is 1/3. So "unlikely" (since likely would be more probable, like more than half). So the answer for Bag A is "unlikely".

Bag B:

Step1: Analyze Bag B's marbles

Bag B has 2 red, 4 blue marbles. No yellow marbles. So picking a yellow marble: probability 0. So it's "impossible".

Bag C:

Step1: Analyze Bag C's marbles

Bag C has 4 yellow, 1 red, 1 blue. Total = 6. Yellow marbles: 4. Probability of yellow: $\frac{4}{6}=\frac{2}{3}≈0.67$. Since 0.67 > 0.5, so it's "likely".

Answer:

Bag A: unlikely
Bag B: impossible
Bag C: likely

(For each bag, the correct options are:
Bag A: ○ unlikely
Bag B: ○ impossible
Bag C: ○ likely)