Are the following events independent or dependent?

Pulling a card out of a deck, and then pulling out a second card without replacing the first one.

A master criminal known as "The Thief" steals your diamond. Legend has it that he has never been caught. You, however, have urgent need of that diamond. (Plus, it was, like, at least the cost of two cows.) You go on a quest to retrieve the diamond!

You can choose from 8 melee weapons, 3 shields, and 2 bows. If you take one of each, how many adventure gear groups are possible?

Upon approaching a tavern with a secret club to gather information, the guard asks you to answer the following to enter:

Can ye evaluate P(12, 12)?

The guard is still unconvinced. He asks:

But can ye evaluate C(12, 12)?

You enter the tavern and ask for information on The Thief. You are promised the information only if you are randomly selected in a secret group.

Out of the 20 people in the tavern, only 3 people will be selected for the secret group. How many different groups are possible?

You find out where The Thief was last seen, and decide to relax at the tavern for a bit. You overhear somebody telling a story:

"So there was 12 horses in a race. I won the grand prize by guessing which horses got in 1st, 2nd, 3rd, 4th, and 5th place correctly. That's how I got all this gold!"

How many different race results are possible with 12 horses, and you care about which ones got in 1st, 2nd, 3rd, 4th, and 5th place?

You confront the man and tell him that there is very little chance he could have guessed the correct outcome of the horse race. He sweats a little bit and confesses:

"Aye, yer right. All I had to do was guess which 5 horses would cross first, not caring about the order."

If there are 5 horses being chosen out of 12 horses, how many groups are possible?

You're still skeptical that he could have guessed that correctly, and ask him where he really got his gold from. He glares at you, and then bolts for the door. You chase him, and find that he is running to the exact location that you heard The Thief was seen. You turn the corner to see a door slam shut.

There is a lock on the door where you have to insert 3 red shapes and 3 blue shapes in a row (each is a different shape). If you have to alternate between red and blue, starting with a red shape, how many different arrangements are possible?

You try different lock combinations, and find the correct one after a bit. Breaking into the building, you find that it is a vast lair. There are 5 doors each with a number written above. The doors are labeled 1, 2, 3, 4, and 5. A sign reads "To open the doors, one must speak aloud the standard deviation of their numbers rounded to the nearest tenth."

After realizing that's the stupidest puzzle you ever heard, which number do you say?

The sign also says, "The correct doors are the median or the mean of these numbers." You boldly go through door number 3 because...

(Note: the doors are labeled 1, 2, 3, 4, and 5.)

You finally find the man you were chasing, and says "Do you think you can outsmart The Thief?!" and he hides your diamond in a random box amongst a group of boxes that form the shape of a bell curve (normal distribution).

You really don't have time for this, so you only search from the 80th box to the 120th box. If the mean box is 100, and the standard deviation is 10, what is the percent chance that you will find the diamond in this search?

You finally have the diamond, and you bring it to the person you plan to wed after you imprison The Thief (who was a whole lot less cool than you thought he'd be). Unfortunately they'll only marry you if the conditions are perfect. You quickly try to find the likelihood that the temperature will be perfect tomorrow.

The mean temperature of this month is 80⁰ and the standard deviation is 4.2^o. What is the percent chance that the weather will be at least 75.8^o?