20 ! scenario 1: you and a friend take turns choosing marbles at random from a jar containing 13 red marbles and 13 blue ones. once you select a marble, you record the color of the marble and do not return the marble to the jar. scenario 2: you and a friend take turns choosing marbles at random from a jar containing 13 red marbles and 13 blue ones. once you select a marble, you record the color of the marble and return the marble to the jar. a) identify each scenario as independent or dependent. explain your answer. b) are the probabilities of selecting two blue marbles in each scenario the same or different? explain your answer.

Scenario 1 is dependent. Each time you draw from the jar, the selection changes because you’re not replacing the previous marble. Scenario 2 is independent because the marbles are put back in the jar, so the odds do not chance.

In scenario 1, you have a 13/26 (50%) chance of selecting a blue marble. Now that you’ve removed that blue marble, there are now 13 red and 12 blue, so your chance of getting blue is 12/25 (48%). So your chance of getting two blue in a row is 13/26 x 12/25= .5 x .48= .24= 24%. Whereas in scenario 2, you have a 13/26 chance of getting a blue marble each time. So your chance of getting two blue in a row is 13/26 x 13/26= .5 x .5= .25= 25%. So you have a higher chance (by 1%) of getting two blue in a row in scenario 2 than 1