1. ## Easy probability problem...

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?

Thanks.

2. Originally Posted by PandaPanda
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. Mr F says: Correct.

At minimum, you only need to draw one card to have a chance of getting a club, right? Mr F says: Correct.

At most, you might need to draw 19 cards, because in some unlikely situation, you could draw every other card before a club.

Mr F says: Are you putting the card back after each draw? If so then you're correct. If not (and what I've noted in blue suggests this), then ........

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?

Mr F says: What does the stuff in blue say? When sampling without replacement the draws are not independent. The outcome of one draw will affect the outcome of the next.

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?

Thanks.
You are treating the question as if the cards are not replaced after each draw. The question clearly states that they are.

The questions do not require any specialist knowledge of Euchre by the way.

3. Thanks for the feedback.
Here's my misunderstanding in the context:

What card is replaced? If it's the deck, what is it replaced with, the card that was drawn? Thanks.