Probabilities for choosing these outcomes Quiz by bigalsirkp

Drawing one card from a regular deck
P(Jack)
P(Higher than a 10)
P(Red card)
P(Not lower than a 5)
P(Not a black 3)
P(Black card or higher than a Jack)
P(Not a diamond)
P(Not a Heart and higher than a 7)
P(Queen of diamonds and a King)
P(King or red 3)

Rolling 2 fair dice
P(Sum of 6)
P(Sum of 3 or 9)
P(Sum of less than 9)
P(Sum of more than 1)
P(Both rolls the same)
P(Difference of 2 between the rolls)
P(Sum a factor of 24)
P(Product of 12 and sum of 7)
P(Difference of 1 and sum of more than 5)
P(Sum of 2)

3 fair coins tossed
P(Not 3 heads)
P(At least two tails)
P(Equal number of heads and tails)
P(Not more than 1 tail)
P(First 2 tosses are different)
P(Not 2 heads and 1 tail)
P(3 tails)
P(First and last toss the same or 1 head)
P(Not a head in the middle toss)
P(Less than 5 heads)

Drawing two cards from a standard deck with replacement
P(Exactly 1 Queen)
P(Both a diamond)
P(One black card and one heart)
P(An ace or a King appears)
P(Both cards are different)

Toss 4 fair coins
P(2 heads and 2 tails)
P(All the same)
P(Exactly 3 of either heads or tails)
P(No consecutive tosses the same)
P(An odd number of heads)

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There are 54 comments for this game.
(Warning: comments may contain spoilers)

Probability Quiz

by bigalsirkp

Created Nov 4, 2009 in Science
Game Plays 837

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	mbc:	Nov 17th, 2009 at 10:44 GMT		3 points
	Really enjoyed this. Didn't spot any mistakes either.

	bigalsirkp:	Nov 17th, 2009 at 20:39 GMT		2 points
	Thank you :D Despite your comment it hasn't really been taken very much so feel free to publicise...

	hscer:	Dec 14th, 2009 at 04:32 GMT		5 points
	May you clarify P(Queen of diamonds and a King)? It seems like a trick question. You said we were taking 1 card from a deck and then you ask about taking out 2 cards. At least, from my perspective.

	RandallPinkston:	Dec 14th, 2009 at 04:54 GMT		4 points
	I'm not sure what you mean by P(Both cards are different). Does that mean that they're different numbers or different suits?

	betraisefold:	Dec 14th, 2009 at 06:13 GMT		2 points
	Very well done, should be a decent challenge for the majority of people, I'm curious to see what the results page will look like after a large number of plays. Finding a better way to distinguish the header question other than the asterisks would help the look and you missed the word card in P(black card or a higher than a jack) @Randall: either (or both):it just means you didn't draw the same card twice.

	micah:	Dec 14th, 2009 at 08:08 GMT		2 points
	I agree that the format could use a bit of work. Other than that, this is a really good quiz--if you can iron out the formatting it seems front-page worthy to me.

	peanut4:	Dec 14th, 2009 at 13:13 GMT		1 point
	Nice idea, but after about six questions, I felt it was back at school doing my homework.

	mjkelly42:	Dec 14th, 2009 at 14:06 GMT		2 points
	You could use the third column to describe the scenario, then have sporcle group questions based on that third column. That would clarify the instructions, although I thought they were fairly intuitive if you just go in order.

	Probus:	Dec 14th, 2009 at 16:40 GMT		0 points
	The probability of drawing (any) one card is 1/52. The probability of drawing one card to a particular value is 1/13.

	simo:	Dec 14th, 2009 at 19:53 GMT		2 points
	great quiz

	bigalsirkp:	Dec 14th, 2009 at 20:25 GMT		2 points
	@hscer: You are precisely correct - I guess there is a trick in the question. Drawing one card from a deck it is impossible to get a queen of diamonds and a king so therefore the probability is 0 - ie there is no single card that has both queen of diamonds and king (obviously)

	bigalsirkp:	Dec 14th, 2009 at 20:31 GMT		2 points
	@micah: Thanks for the positive feedback. Do you have any suggestions for how to improve the format - not so skilled on computer use in this way?

	leftyfreak:	Dec 14th, 2009 at 21:30 GMT		2 points
	This PhD in statistics enjoyed the quiz! I think drawing the cards without replacement at the end would be more interesting, and more like what happens in real life.

	micah:	Dec 14th, 2009 at 21:34 GMT		2 points
	The best format would be something like this quiz, I think: http://www.sporcle.com/games/agame.php. I suspect that this is the result of what mjkelly is describing, though I'm not familiar enough with sporcle's quiz markup to be sure...

	bdon:	Dec 14th, 2009 at 22:24 GMT		3 points
	Ya, there's a button in the main quiz creation page that allows you to group by hint. You would then have to make all the hints explain the situation and move your exact clues into the third column. I think it's a great quiz as is, but if you are looking to improve it, that would be my recommendation

	Psycho:	Dec 16th, 2009 at 14:45 GMT		2 points
	Awesome quiz. I hope that using a calculator is not considered cheating.

	simpleerrors:	Dec 19th, 2009 at 14:53 GMT		2 points
	I hope using pen and paper isnt cheating. Got stuck on the "ace or king appears". anyone care to explain that? and the whole 0 and 1 I forgot about them, so the trick one confused me.

	bigalsirkp:	Dec 19th, 2009 at 18:54 GMT		2 points
	Using a pen and paper is not cheating. Say you pick the Ace of diamonds out first. Then there are 52 ways of doing that (one for each card in the deck - including the ace of diamonds). That means there are 51 ways of picking the ace of diamonds out as the second card as we have already counted the ace of diamonds followed by the ace of diamonds. Say you next pick out the Ace of clubs. There are 51 ways of doing that as we have already counted the ace of clubs followed by the ace of diamonds. Then there are 50 ways of picking out the ace of clubs as the second card as we have already counted ace of clubs followed by ace of clubs and ace of diamonds followed by ace of clubs. Continue the pattern for each of the 8 ace and king cards and you are left with... 52+51+51+50+50+49+49+48+48+47+47+46+46+45+45+44 = 768 ways. Now that is out of 2704 total ways seeing as there are 52 options for the first card and 52 options for the second card. 768/2704 simplifies nicely to 48/169. Alternatively and much easier to see is consider just one suit (say the spades.) 13 ways of picking ace of spades as the first card, 12 ways of picking ace of spades as the second card as we have already counted ace of spades and ace of spades. 12 ways of choosing king of spades as first card, as we have already counted king of spades and ace of spades. 11 ways of choosing king of spades as second card as we have already counted king of spades followed by king of spades and ace of spades followed by king of spades. (13+12+12+11)/(13*13) = 48/169 :)

	LetsGoBlue:	Dec 19th, 2010 at 05:45 GMT		2 points
	Yet one more way to think about ace or king appears is to note that it can happen on either the first or second pull. So on pull 1, p(A or K)=2/13 (4 aces, 4 kings=8/52=2/13). Or, we can get something other than an ace or king on pull 1 (p=11/13) and an ace or king on pull 2 (again, p=2/13). So the total is p=2/13+(11/13)(2/13)=2/13+22/169=26/169+22/169=48/169.

	Manticore:	Jan 4th, 2011 at 13:26 GMT		3 points
	Really enjoyed this quiz. But it would be helpful to specify that aces are high. In some contexts, they count as less than 7, etc.

	trisy123:	Dec 14th, 2012 at 18:17 GMT		0 points
	i didnt do very well because i only got 8/40 which was bad

	fletch7:	Dec 15th, 2012 at 11:00 GMT		2 points
	it took a couple of goes but i got there in the end

	hcoxkr6:	Dec 15th, 2012 at 19:28 GMT		2 points
	Same as fletch7 really

	AxtonTheCommando:	Dec 15th, 2012 at 22:16 GMT		1 point
	boom, took a few tries, only one who chose an awesome username, borderlands 2 character k.mitchell

	ihatemaths:	Dec 16th, 2012 at 08:44 GMT		2 points
	Although I hate maths I did quite well :)

	hcoxkr6:	Dec 16th, 2012 at 09:28 GMT		0 points
	Lol, who's I hate maths?

	marble2748:	Dec 16th, 2012 at 09:58 GMT		0 points
	from cdc it was very hard i think i got nine

	Harriet_Jarrome:	Dec 16th, 2012 at 12:28 GMT		2 points
	Didn't do too bad some of the questions confused me though

	bigalsirkp:	Dec 16th, 2012 at 12:44 GMT		-1 points
	Yeh, a pencil and paper to list the outcomes or draw a tree diagram is necessary here...

	passyx23:	Dec 16th, 2012 at 16:07 GMT		2 points
	did quite well didn't understand what it meant by Drawing two cards from a standard deck with replacement?

	bigalsirkp:	Dec 16th, 2012 at 16:51 GMT		0 points
	@passyx23: So you select a card and put it back, then select another card. For example the probability of getting the king of diamonds followed by the king of diamonds would be 1/52 x 1/52.

	Ihatemaths2:	Dec 17th, 2012 at 20:06 GMT		0 points
	Done...

	GeorgiaKate:	Dec 17th, 2012 at 20:31 GMT		2 points
	took ages. the last question confused me and the 6th one if 3 coins tossed confused me to but I did it in the end..

	cdufcbarnnffc:	Dec 19th, 2012 at 18:09 GMT		2 points
	I did okay, i got just above 1/4 of them and tried it a couple of times before getting some right in the end. try again another time.

	gbs9:	Dec 19th, 2012 at 19:40 GMT		2 points
	I did it and got 15

	XIDANIX:	Dec 20th, 2012 at 20:01 GMT		2 points
	I did ok

	Kawaiidaisypetal:	Dec 23rd, 2012 at 19:27 GMT		2 points
	I think i did okay for probability but i couldn't remember how to do the questions with the pack of cards.

	mtmukdk:	Jan 4th, 2013 at 09:51 GMT		2 points
	It took me a couple of goes to get the score that I got in the end, and I am fairly pleased with it, but I struggled a little with the section about the replacement cards because they are larger figures, but I think that if I wasn't limited on time, I would have achieved more. Thank you.

	Adam_Hassell:	Jan 4th, 2013 at 11:12 GMT		2 points
	I did ok, but what does it mean by 'with replacement'? Didn't understand that even with the answers there.

	Slj6907:	Jan 5th, 2013 at 15:28 GMT		2 points
	I took me about 7 tries but got 34/40 in the end. Didn't really understand with replacement either to be honest...