Question

There are two bags containing only purple and green marbles.Bag A has 4 purple marbles and 16 green marbles.Bag B has 3 purple marbles and 9 green 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 purple or green marble from Bag A.Event 3: choosing an orange marble from Bag B.Event 4: choosing a purple marble from Bag A.Least likelyMost likelyEvent |Event EventEvent

Answer 1

We need to find the probability of each event, and then list them from the least to the most likely event.

The probability of each event is found by dividing the number of marbles of the described colors by the total number of marbles in that bag.

The number of each marble in each bag is:

• Bag A: 4 purple, 16 green

,

• Bag B: 3 purple 9 green

So, we obtain:

`\text{Probability of event 1: }(3)/(3+9)=(3)/(12)=(1)/(4)`
`\text{Probability of event 2: }(4+16)/(4+16)=(20)/(20)=1`
`\text{Probability of event 3: }(0)/(3+9)=0`
`\text{Probability of event 4: }(4)/(20)=(1)/(5)`

Now, notice that:

`0<(1)/(5)<(1)/(4)<1`

Therefore, ordering the events from the least to the most likely one, we obtain:

Event 3, Event 4, Event 1, Event 2