Question

A bag has 12 different-colored marbles: 4 green, 5 blue, 1 yellow, and 2 orange. You draw a marble from the bag. If you get an orange marble or yellow marble, you win a prize.

Answer these questions:
a. What is the theoretical probability of winning the game? Show your work..

b. What is the most likely outcome? Use probabilities to support your answer, and show your work.

c. What is the least likely outcome? Use probabilities to support your answer, and show your work.

d. Is it more likely that players will win or lose playing the game? Explain why.

Answer 1

The theoretical probability of winning the game is 0.25. The most likely outcome is drawing a blue marble and the least likely outcome is drawing a yellow marble. It is more likely for players to lose playing the game.

Step-by-step explanation:

a. The probability of winning the game is the ratio of favorable outcomes to total outcomes. In this case, the favorable outcomes are getting an orange marble or a yellow marble, which is 1 yellow marble + 2 orange marbles = 3 favorable outcomes. The total outcomes are the number of marbles in the bag, which is 12. So the probability of winning is 3/12 = 1/4 = 0.25.

b. The most likely outcome is drawing a blue marble, as there are 5 blue marbles in the bag. The probability of drawing a blue marble is 5/12 = 0.4167.

c. The least likely outcome is drawing a yellow marble, as there is only 1 yellow marble in the bag. The probability of drawing a yellow marble is 1/12 = 0.0833.

d. It is more likely for players to lose playing the game. This is because the probability of winning is 0.25, which is less than the probability of losing (1 - 0.25 = 0.75).

Answer 2

Step-by-step explanation:

4+5+1+2=12

1+2=3

4+5=9

12 - all marbles

4 - green marbles

5 - blue marbles

1 - yellow marble

2 - orange marbles

3 - yellow and orange marbles

9 - green or bule marbles

a.
`(3)/(12)` win only when draw 1 yellow or 1 of 2 orange.

b.
`(5)/(12)` the mostly likly outcom is for blue marbles, (more than other colour in bag)

c.
`(1)/(12)` the least likly outcom is for yellow marble, (less than other colour in bag)

d.
`(9)/(12)` propability of lose

`(9)/(12) > (3)/(12)` player will lose more likly than win.