For problems 1-4, decide if the events are independent or dependent. Justify your answer.

1.) Picking a 3 from a standard deck of cards, replace it, and then select another 3 from the deck. Justify:

2.) You're dealt two cards from a standard deck. The first card is an Ace and the second card is a King. Justify:

3.) Roll a six-sided die and then roll it again to achieve a sum of eight. Justify:

4.) A red marble is selected from a bag, replaced, and another red marble is selected. Justify:

In the general population, 9 out of every 100 people will develop type 2 diabetes. 1 in 600 US adults carries a gene that makes them more susceptible to developing type 2 diabetes. 8 out 10 people who carry this gene develop type 2 diabetes. Show your work and use the correct probability notation for the following:

5.) Calculate the probability that a randomly selected US adult will develop type 2 diabetes given that they have the gene:

6.) Calculate the probability that a randomly selected US adult carries the gene and debvelops type 2 diabetes:

7.) Are the events of carrying the gene and developing type 2 diabetes independent? Explain

.

In a sample of 2000 US adults 215 are found to be left handed. Three people are selected at random without replacement. Show your work and use the correct probability notation for the following:

8.) Find the probability that all 3 are left-handed:

9.) Find the probability that all three are not left-handed:

10.) Find the probability that at least one of the selected is left-handed: