Question

There are two bags containing only white and blue marbles

Answer 1

We are giving the following events:

Event 1: choosing a blue marble from bag B

Event 2: choosing a white marble from bag B

Event 3: Choosing a purple margle from bag A

Event 4: choosing a white marble from bag A

To calculate the probability of each event, we will simply apply the following principle: we will count the number of possibilities we have to make the event true, and divide it by the total number of marbles of that bag.

Let us calculate the probability of event 1 to illustrate this principle.

Event 1:

Consider bag B. It has 6 white marbles and 2 blue marbles, for a total of 8 marbles. As we want to consider all posibilities of choosing a blue marble, we only have 2 possibiilited to make this event true. So, applying the principle we have that

`P(E_1)=(2)/(8)=(1)/(4)=0.25`

Event 2:

As we want to choose a white marble from bag B, there are 6 possibilites from where we can choose a white marble. THus, we have that

`P(E_2)=(6)/(8)=(3)/(4)=0.75`

Event 3:

Since there are no purple marbles in bag A, there are no possibilites for event 3 to occur. So we have

`P(E_3)=(0)/(20)=0`

Event 4:

We want to choose a white marble from bag A. There are 11 white marbles in bag A and 20 marbles in total. Then, the probability would be

`P(E_4)=(11)/(20)_{}=0.55`

Using this information, if we ordered the events based on their likeliness (or probability) form least to most likely, we would have

Event 3, Event 1, Event 4 and Event 2E