# Lottery ticket problem (probability)

1. Mar 11, 2008

### mymaydayya

An instant lottery ticket consists of a collection of boxes cpvered with gray wax. For a subset of the boxes, the gray wax hides a special mark. If a player scratches off the correct number of the marked boxes (and no boxes without mark), then that ticket is a winner, Design an instant lottery game in which a player scratches five boxes and the probability that a tickert is a winner is approximately 0.01.

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my answer:(1/2)^n * (n choose 5) =0.01

is it right? thans~

2. Mar 11, 2008

### tiny-tim

Hi mymaydayya! Welcome to PF!

Hint: if there are n boxes, and 5 are marked, then:

how many ways are they of choosing 5 boxes?

How many of them will be winners?

Divide one by the other …

3. Mar 11, 2008

### mymaydayya

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how many ways are they of choosing 5 boxes? (n choose 5)

How many of them will be winners? 1

but there is no approxite answer to 0.01

I don't know well how this game is porcessed, so I guess that players don't know how many boxes to scratch.

4. Mar 11, 2008

### tiny-tim

Well, you want n choose 5 to be about 100.

So you want n(n-1)(n-2)(n-3)(n-4) to be about 5! x 100, = 12000.

And the fifth root of 12000 is about 6.5.

So try n = 8, then n choose 5 = 8.7.6/1.2.3 = 56;
then try n = 9, n choose 5 = 9.8.7.6/1.2.3.4 = 126, which is nearer!

Of course, you could have a lottery in which there are 6 marked boxes, and you scratch 5 …