# Probability Problem

## Posers and Puzzles

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Quiz Master
###### Quiz Master
21 Feb 15

An NZ supermarket chain is offering collectable cards with purchases.

With every \$10 spent you get 4 cards (all different).

There are 108 cards to collect.

How much do you have to spend before you are likely
(better than 50% chance) to obtain a set?

This is a real problem and I'm very keen to know the answer!

THANKS

21 Feb 15

These are not computations you can do by hand. If we believe Wolfram|Alpha, that would be about 550 cards: http://www.wolframalpha.com/input/?i=108!*S2%28k%2C108%29%2F108^k+from+k%3D500+to+600

###### Fast and Curious
21 Feb 15

Originally posted by WanderingKing
These are not computations you can do by hand. If we believe Wolfram|Alpha, that would be about 550 cards: http://www.wolframalpha.com/input/?i=108!*S2%28k%2C108%29%2F108^k+from+k%3D500+to+600
So that would mean you need to spend \$1375 to get 50%.

###### Quiz Master
21 Feb 15

Originally posted by sonhouse
So that would mean you need to spend \$1375 to get 50%.
Yes it's a nice little ploy by the Marketing People!
Especially as the cards are aimed at children and you know how they like to collect cards!
http://www.countdown.co.nz/superanimals

22 Feb 15
4 edits

Did a small perl simulation of this:
Over 10000 successes, min money was £670, max was £3460, mean was £1,409.78, median was £1,350 and stddev was £336.62

Over 100000 successes, min money was £650, max was £4490, mean was £1,404.93, median was £1,350 and stddev was £335.05

So the answer seems pretty stable, I would expect to pay the median of £1,350, although as the large max shows, you can pay a lot more if you are unlucky with getting the last card.

Of course the vastly most efficient way is to collaborate with other collectors by swapping your duplicates for ones you do not have.
http://www.countdown.co.nz/superanimals/swapzone

And, as a possible downside, often with these things there are not equal probabilities of getting each card.

22 Feb 15

Originally posted by wolfgang59
Yes it's a nice little ploy by the Marketing People!
Especially as the cards are aimed at children and you know how they like to collect cards!
http://www.countdown.co.nz/superanimals
Oh, we had those over here, too, or something very similar. My nieces and nephew collected the whole set. Not by spending large amounts, mind you - by trading with their classmates. If there's one thing children love even more than collecting cards it's swapping them with their friends.

###### Quiz Master
22 Feb 15

THANKS for all the help guys!!!
It's worse than I thought because it's a \$20 spend.
But as pointed out the store have set up a swap zone. :-)

###### Quiz Master
10 Mar 15

Now have 500+ cards.
Need two for first set.
Need 8 for second set.
Promotion finishes in 5 days.
Word on the playground is nobody has a set yet.

###### troll taunter
10 Mar 15

Originally posted by wolfgang59
Now have 500+ cards.
Need two for first set.
Need 8 for second set.
Promotion finishes in 5 days.
Word on the playground is nobody has a set yet.
when I collected such cards in the 60's, us kids were convinced that 'they' held back certain cards until the 'run' had almost finished to keep us buying...

Suddenly, in the last few days, a card that was absolutely non-existant before would 'swamp the market'

I am sure it was just coincidence!!