What is incorrect about the following reasoning? Be specific!

Herman says that if you pick a United States citizen at random, the probability of selecting a citizen from Indiana is because Indiana is one of 50 equally likely states to be selected.
Jerry has set up a game in which one wins a prize if he/she selects an orange chip from a bag. There are two bags to choose from. One has 2 orange and 4 green chips. The other bag has 7 orange and 7 green chips. Jerry argues that you have a better chance of winning by drawing from the second bag because there are more orange chips in it.
Gil the Gambler says that it is just as likely to flip 5 coins and get exactly 3 heads as it is to flip 10 coins and get exactly 6 heads because \[ \frac{3}{5} = \frac{6}{10} \]
We draw 4 cards without replacement from a deck of 52. Know-it-all Ned says the probability of obtaining all four 7’s is because there are ways to select the 4 cards and there are four 7’s in the deck.
At a festival, Stealin’ Stan gives Crazy Chris the choice of one of three prizes—each of which was hidden behind a door. One of the doors has a fabulous prize behind it while the other two doors each have a “zonk” (a free used tube of toothpaste, etc.). Crazy Chris chooses Door #1. Before opening that door, Stealin’ Stan shows Chris that hidden behind Door #3 is a zonk and gives Chris the option to keep Door #1 or switch to Door #2. Chris says, “Big deal. It doesn’t help my chances of winning to switch or not switch.”
2025-03-05 21:34:30