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 one year 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.
 one year 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
 one year 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?

hba
 one year ago
Best ResponseYou've already chosen the best response.0How many cards in a deck ?

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

EulerGroupie
 one year 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
 one year 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
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1I would guesstimate a little less than 1400 to 1

schmidtdancer
 one year ago
Best ResponseYou've already chosen the best response.0hey I'm here now

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

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

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

radar
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0So what would my answers be?

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

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

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

radar
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0Ok so b would then be 12/51?

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

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

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

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

mathmate
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0Thanks! how do i begin c?

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

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

mathmate
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0Its ok. but is 11 right?

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

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

schmidtdancer
 one year ago
Best ResponseYou've already chosen the best response.0I mean 11/50!!!!

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

mathmate
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0so (d) is: 10/49?

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

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

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

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

mathmate
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0so f is then: 11880/23990400??

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

mathmate
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0I have 495/999600 so far

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

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

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

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

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

mathmate
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.04 times as much?@mathmate

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

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

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

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

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

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

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

mathmate
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0Oh oak!! thanks for all your help

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