Question

there are two bags containing only yellow and green marbles. bag a has 4 yellow marbles and 16 green marbles. bag b has 9 yellow marbles and 3 green marbles. a marble is randomly chosen from each bag. list these events from least likely to most likely. event 1: choosing a green marble from bag b. event 2: choosing a black marble from bag b. event 3: choosing a yellow marble from bag a. event 4: choosing a yellow or green marble from bag a. least likely → most likely event , event , event , event

Explanation:

Step1: Calculate probability of Event 1

Bag B has 9 yellow and 3 green marbles, total 12 marbles. Probability of choosing green from Bag B is $\frac{3}{12}=\frac{1}{4}$.

Step2: Calculate probability of Event 2

There are no black marbles in Bag B, so probability is 0.

Step3: Calculate probability of Event 3

Bag A has 4 yellow and 16 green marbles, total 20 marbles. Probability of choosing yellow from Bag A is $\frac{4}{20}=\frac{1}{5}$.

Step4: Calculate probability of Event 4

Since Bag A contains only yellow and green marbles, probability of choosing yellow or green from Bag A is 1.

Step5: Compare probabilities

$0<\frac{1}{5}<\frac{1}{4}<1$, so order is Event 2, Event 3, Event 1, Event 4.

Answer:

Event 2, Event 3, Event 1, Event 4