Question

there are two bags containing only orange and blue marbles.
bag a has 15 blue marbles and 5 orange marbles.
bag b has 12 blue marbles and 3 orange marbles.
a marble is randomly chosen from each bag.
list these events from least likely to most likely.
event 1: choosing a purple marble from bag b.
event 2: choosing a blue marble from bag a.
event 3: choosing a blue or orange marble from bag a.
event 4: choosing a blue marble from bag b.
least likely → most likely
event , event , event , event

Explanation:

Step1: Calculate probability of Event1

Event1: No purple marbles in Bag B, so $P(Event1)=0$.

Step2: Calculate probability of Event2

Bag A total marbles: $15+5=20$. Blue marbles:15. $P(Event2)=\frac{15}{20}=0.75$.

Step3: Calculate probability of Event3

All marbles in Bag A are blue/orange, so $P(Event3)=1$.

Step4: Calculate probability of Event4

Bag B total marbles: $12+3=15$. Blue marbles:12. $P(Event4)=\frac{12}{15}=0.8$.

Step5: Order probabilities

$0 < 0.75 < 0.8 < 1$, so order is Event1, Event2, Event4, Event3.

Answer:

Event 1, Event 4, Event 2, Event 3