Question

there are two bags containing only blue and black marbles bag a has 4 blue marbles and 6 black marbles. Bag b has 6 blue marbles and 14 black marbles.A marble is randomly chosen from each bag. List these events from least likely to most likely.Event 1. choosing a blue or black marble from bag BEvent 2. choosing a blue marble from bag AEvent 3. choosing a blue marble from bag BEvent 4. choosing a yellow marble from bag B

Answer 1

Answer

Arranged from least likely to most likely

- Event 4. choosing a yellow marble from bag B​

- Event 3. choosing a blue marble from bag B

- Event 4 choosing a blue marble from bag A

Explanation

Bag A

4 blue marbles and 6 black marbles.

Bag B

6 blue marbles and 14 black marbles.

So, to arrange given cases in the order of least likely to most likely, we need to find the probabilities of each of them.

Event 1. choosing a blue or black marble from bag B

This would entail picking bag B first, then picking from either blue or black ball first. Since all the balls in the bag are either black. So, the probability is given as

Probability

= (Probability of picking one type of bag) (Probabiliy that the ball is either blue or black)

= (0.5) (1)

= 0.5

Event 2. choosing a blue marble from bag A

Probability

= (Probability of picking bag A) (Probabiliy that the ball is blue from A)

= (0.5) (4/10)

= (0.5) (0.4)

= 0.2

Event 3. choosing a blue marble from bag B

Probability

= (Probability of picking bag B) (Probabiliy that the ball is blue from B)

= (0.5) (6/20)

= (0.5) (0.3)

= 0.15

Event 4. choosing a yellow marble from bag B​

Probabiliity

= ((Probability of picking bag B) (Probabiliy that the ball is yellowfrom B)

= (0.5) (0/20)

= 0.5 (0)

= 0

0 < 0.15 < 2 < 0.5

Hope this Helps!!!