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 2 years ago
Back to the cards! In poker, a flush is when all five cards are the same suit. Find the probability of being dealt a flush (when being dealt five cards).
Start by just considering clubs.
 2 years ago
Back to the cards! In poker, a flush is when all five cards are the same suit. Find the probability of being dealt a flush (when being dealt five cards). Start by just considering clubs.

This Question is Closed

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0a) What is the probability that the first card dealt is a club? b) What is the probability that the second card dealt is a club given that the first one was a club? c) What is the probability that the third card dealt is a club given that the first two were clubs? d) What is the probability that the fourth card dealt is a club given that the first three were clubs? e) What is the probability that the fifth card dealt is a club given that the first four were clubs? f) The probability of being dealt all five clubs is the product of the above probabilities. Why is this true and what is this probability? g) You have now found the probability of being dealt a flush in clubs. This is the same as the probability of being dealt a flush in diamonds, hearts, or spades. Then, what is the proability of being dealt a flush?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Umm... im not sure

EulerGroupie
 2 years ago
Best ResponseYou've already chosen the best response.0There are 52 cards in a standard deck. Divide by 4 to get the number of cards of each suit.

radar
 2 years ago
Best ResponseYou've already chosen the best response.1That would mean there are 13 club cards out of 52 cards. Wouldn't that mean the probability of drawing a club is 1 out of 4?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Yes, drawing the first club out of the full deck of 52 cards has a probability of 1 out of 4, or 0.25. What about the probabiliity of the second card:  how many clubs are left (assuming first one is a club) ?  how many cards are left in the deck?

radar
 2 years ago
Best ResponseYou've already chosen the best response.1Now on the 2nd draw there would be 13 club cards out of 51 3rd draw 12 out of 50 4th draw 11 out of 49 5th draw 10 out of 48

radar
 2 years ago
Best ResponseYou've already chosen the best response.1Wouldn't that be the chances for each draw assuming he draws into a 5 card flush. Now take the product of all those chances to get the probability. 1/4 * 13/51 * 6/25 * 11/49 * 5/24

radar
 2 years ago
Best ResponseYou've already chosen the best response.1I would guesstimate a little less than 1400 to 1

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0so a i got 1/4. what is b?

radar
 2 years ago
Best ResponseYou've already chosen the best response.1Chance according to Google is 0.003940. or about 254 to 1 so it looks like I probably erred.

radar
 2 years ago
Best ResponseYou've already chosen the best response.1I am afraid I have been away from those kind of problems too long. Hopfully, @mathmate will provide further assistance.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Do u know anyone online right now that can give me assistance now?

radar
 2 years ago
Best ResponseYou've already chosen the best response.1The Google solution involved a flush in any suit not just clubs.

radar
 2 years ago
Best ResponseYou've already chosen the best response.1The probability of a flush can occur in hearts, diamonds, spades or clubs, just as long as all cards are the same suit!

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0So what would my answers be?

radar
 2 years ago
Best ResponseYou've already chosen the best response.1You requested the probability of a flush in clubs only.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Yea. thats what the question said

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0how would I start answering B?

radar
 2 years ago
Best ResponseYou've already chosen the best response.1I answered that, if the first one was a club, you now have a deck of 51 cards of which 12 are clubs; 12/51 or 0.235294

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Ok so b would then be 12/51?

radar
 2 years ago
Best ResponseYou've already chosen the best response.1Here is mathmate. hopefully shed some light on this.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0I have (a) 1/4 (b) 12/51 now c?

radar
 2 years ago
Best ResponseYou've already chosen the best response.1Ask yourself how many cards are now in the deck, how many are clubs and figure out the probability using the method you have been taught.

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Sorry for being away. @radar sorry, I was just questioning in case there was a typo. For (b) After the first card, there are 131=12 clubs left out of 51. So the probability is 12/51. Or, using conditional probabilities: P(1)=13/52 P(1&2)=13/52*12/51 P(21)=P(2&1)/P(1)=(13/52*12/51) / (13/52) = 12/51, same as before.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Okay I got that for (b) too!:) Im not sure how to find c now

radar
 2 years ago
Best ResponseYou've already chosen the best response.1Sorry but I have to now run, you are in good hands.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Would (c) be 11/51 then?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2@schmidtdancer The questions are made in such a way to guide you to the final answer. I suggest that after a and b have been explained and answered, it would be advantageous for you to continue the logic and post your suggested responses for verification. What do you think?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0? I just need clarification on how to find C. can u guide me through the steps....and ill figure it out by myself then u can check?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks! how do i begin c?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0c) What is the probability that the third card dealt is a club given that the first two were clubs?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2For the third club in a row, how many clubs are left? and how many cards are left in the deck?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0since there are 14 clubs in a set, then we would have 11 left right?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0because b is 12/51? and were losing another so would c be 11/51?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2I'll make it clear: After the first two clubs are drawn and before we draw the third card, how many clubs remain in the deck, and how many cards total remain?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0there are 14 clubs total in a deck... and 52 cards total in a deck... so, after two are drawn, then we have 12 clubs and 50 cards?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0is that for b or c?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Each deck has 52 cards, divided by 4 suits gives 13 cards per suit to start with (not 14). (a) before drawing any card, we have 13 clubs and 52 cards. (b) given the first card drawn was a club, before drawing the second card, we have 12 clubs and 51 cards. (c) given the first 2 cards drawn were clubs, before drawing the third card, we have how many clubs and how many cards in the deck?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2We have only drawn 2 clubs out of 13, how many left?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Sorry, the OS seems to be very selective in response. I cannot get to your question unless I go by your profile. When I go by "mathematics", it never responds for the past two days.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Its ok. but is 11 right?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2(c) Also, drawn two cards (clubs) out of 52, how many left?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0so 11/52 would be c?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Yes, that is correct for (c). Again, your response was not updated. I had to check through you profile every time I suspect a response. You're comfortable continuing?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0How would I find (d) now @mathmate

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Each deck has 52 cards, divided by 4 suits gives 13 cards per suit to start with (not 14). (a) before drawing any card, we have 13 clubs and 52 cards. (b) given the first card drawn was a club, before drawing the second card, we have 12 clubs and 51 cards. (c) given the first 2 cards drawn were clubs, before drawing the third card, we have how many clubs and how many cards in the deck? (d) given the first 3 cards drawn were clubs, before drawing the fourth card, we have how many clubs and how many cards in the deck?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0so (d) is: 10/49?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0This is what I have.... is it correct @mathmate ? (a) 1/4 (b) 12/51 (c) 11/50 (d) 10/49 (e) 9/48

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Looks good so far. Keep it up, you're almost there!

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Im a little confused on f and g!

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Have you done conditional probability before?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0When it says product, do I just multiply ae?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Yes, the numerical part is just the product of the 5 probabilities. Give me a minute for the explanation part of (f). Once you have the numerical probability of clubs obtained in (f), how would you propose to find (g)?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0so f is then: 11880/23990400??

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Then would g be the decimal value of f?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2It's almost correct, but you need to simplify it to the simplest form. Can you do that?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0I was gonna ask u lol, I'm not sure how to simplify it... im trying

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2No. Think of (g) is for the case where there are 4 suits instead of just clubs. Imagine buying raffle tickets. What are the changes of winning if you bought 4 instead of one?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0I have 495/999600 so far

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Is this f?? 33/66640

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Factors that you can cancel are like 36...

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0is this right @mathmate 33/66640

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Ok thank you! now, g?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0g) You have now found the probability of being dealt a flush in clubs. This is the same as the probability of being dealt a flush in diamonds, hearts, or spades. Then, what is the proability of being dealt a flush?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0im not sure what its asking for an answer....@mathmate

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Means a flush of any of the 4 suits. Imagine buying raffle tickets. What are the changes of winning if you bought 4 instead of one?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.04 times as much?@mathmate

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Right! That's. I hope you are better prepared for the next question.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0But what would g be??

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Is the answer: 4 times as much? @mathmate

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.24 times what you got for (f).

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0132/266560 in fraction form < is this the answer @mathmate

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2I would rather put it as 4*(33/66640) =33/16660. In probabilities, small numbers like 0.002 is better represented by fractions.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0thx! so g @mathmate is 33/16660?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0but thats lower than f.

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2Yes. I am sorry it is probably painful for you as much as for me because the system does not respond (does not update). So I don't really know when you put in a response.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0its ok but @mathmate how is g 33/16660? when f is higher than that value?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2When the denominator is 4 times smaller, it means that the fraction is 4 times bigger. For example, 1/4 is smaller than 1/1.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Oh oak!! thanks for all your help

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.2You're welcome! Good luck with your homework/exam! :)
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