Got my first math assignment this week and already I don't know what to do o_O
Here it is (mostly I'm struggling with context, etc.)
1. Euchre is a popular card game played with a partial deck of ordinary cards. Only 24 cards are used: the 9, 10, Jack, Queen, King, and Ace of each suit. Consider the experiment of drawing cards from a Euchre deck until a club is drawn. After each draw, the card is replaced and the deck is shuffled.
a. What is the probability of drawing a club on the first draw? Find the smallest and the largest number of cards you might need to draw to get a club.
Here's my confused answer: The probability is 25% since clubs make up one-fourth of all 24 cards. At minimum, you only need to draw one card to have a chance of getting a club, right? At most, you might need to draw 19 cards, because in some unlikely situation, you could draw every other card before a club.
b. Are the draws independent? Explain
I said yes, since draws rely solely on luck and no other factor. But of course, eventually you run out of cards to replace the deck, so that might be a dependent variable, right? Heck, I don't even know if you keep the cards you draw or not in a game of Euchre. Someone help me out here?
c. Complete the table below for a theoretical probability distribution for the number of draws to get a club.
Number of Draws to Get First Club ... Probability
1 ................ ___
2 ................ ___
3 ................ ___
4 ................ ___
5 ................ ___
6 or more .... ___
Does it go something like: 6 out of 24, then 6 out of 23, 6 out of 22, 6 out of 21, etc. etc? I don't think that's how it works because the problem emphasizes that "the deck is shuffled and the card is replaced." I don't get how that works. So you return your card to the deck? How many cards in a partial deck?