# Probability Question

Discussion in 'Mathematics' started by 1033, Jan 27, 2011.

1. ### 1033

A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up or face down. The total value of the cards which landed face up is then calculated. (Card values are assigned as follows: Ace=1, 2=2, ... , 10=10, Jack=11, Queen=12, King=13. There are no jokers.)

What is the probability that the total value is divisible by 13?

2. ### 1033

A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up or face down. The total value of the cards which landed face up is then calculated. (Card values are assigned as follows: Ace=1, 2=2, ... , 10=10, Jack=11, Queen=12, King=13. There are no jokers.)

What is the probability that the total value is divisible by 13?

3. ### DMNew commenter

What have you done so far? It is no coincidence that 13 is prime.

4. ### florapost

erm - is this a project? competetion entry? challenge to us?

5. ### 1033

just a random challenge to the maths forum...

Was looking for a fun maths problem to do, haven't done it myself yet as i'm trying to plan tomorrow's lessons!

6. ### florapost

what year/ability group were you thinking of aiming it at?

7. ### 1033

the other teachers in my department studentwise - depends on how long it takes us to answer!

9. ### GodOfBiscuitsNew commenter

As a starting point, the number of combinations of how the cards lie is going to be 2^52 = 4.5E15

All we need to do now is try every combination to see if it matches any one of the 28 multiples of 13 we can get from the cards.

It's gonna be a long night.....

10. ### AutumnGirlSoup

I'll start us off:
K
KK
KKK
KKKK
QA
QAQA
QAQAQA
QAQAQAQA
J2
J2J2
J2J2J2
J2J2J2J2
10 3
10 3 10 3
10 3 10 3 10 3
10 3 10 3 10 3 10 3
9 4
9 4 9 4
9 4 9 4 9 4
9 4 9 4 9 4 9 4
8 5
8 5 8 5
8 5 8 5 8 5
8 5 8 5 8 5 8 5
7 6
7 6 7 6
7 6 7 6 7 6
7 6 7 6 7 6 7 6
K Q A
K J 2
K 10 3

well, it is more interesting than the washing up...

11. ### DMNew commenter

KKK?
I knew it was only a matter of time before people with flaming torches turned up.

12. ### ResourceFinder

This discussion may put me off playing pyramid solitair

13. ### florapost

have you seen the pyramid rubiks cube?
(oh - going off topic - what will the topic police say?)

14. ### GodOfBiscuitsNew commenter

to make matters more complex,
K
is really K hearts, K spades, K clubs, K diamonds
QA is Qh,Ah Qh,As Qh,Ac Qh,Ad

15. ### NazardNew commenter

I would say that is fine ... as long as you aren't planning to post lots of faeces that subsequently gets the thread pulled!

16. ### NazardNew commenter

What shape is it?

17. ### AutumnGirlSoup

Erm, what about if we multiplied each unique type-of-card-combination (i.e. KQA but not KK) by 4^n where n is the number of cards - does that help at all?*
@ DM

* Be gentle with me if that is complete garbage - I have a splitting headache and should probably have gone to bed an hour ago.

18. ### DMNew commenter

Why are there no painkillers in the jungle?

Because the parrots eat 'em all.

19. ### GodOfBiscuitsNew commenter

Multiplying by 4^n does help with the unique combos, but there's a lot more more combos that use multiple cards than use four unique ones.

6,6,A
6,3,3,A
6,2,2,2,A
6,5,A,A
6,3,2,A,A
6,4,A,A,A
6,2,2,A,A,A
6,3,A,A,A,A

20. ### AutumnGirlSoup

DM - I shall have to remember that one.

Does order matter?
i.e.are we counting 6h6sAh as different to
6s6hAh?

'cos could we use nCr or nPr to help?