Lottery ticket problem (probability)

In summary, an instant lottery game can be designed where a player scratches 5 boxes out of a collection of 9 boxes covered in gray wax, with a probability of approximately 0.01 that the ticket will be a winner. This is achieved by having 126 ways to choose 5 marked boxes out of 9, giving a probability of 1/126 or approximately 0.008, which is close to the desired probability. Alternatively, a game with 6 marked boxes and a player scratching 5 can also give a similar result.
  • #1
mymaydayya
2
0
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~
 
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  • #2
mymaydayya said:
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.

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

is it right? thans~

Hi mymaydayya! Welcome to PF! :smile:

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 … :smile:
 
  • #3
tiny-tim said:
Hi mymaydayya! Welcome to PF! :smile:

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 … :smile:

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

How many of them will be winners? 1

answer :1/(n choose 5)

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
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! :smile:

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

1. What is the lottery ticket problem?

The lottery ticket problem is a mathematical concept that involves calculating the probability of winning a lottery or other random event. It is also known as the lottery paradox or the paradox of the unexpected hanging.

2. How is the probability of winning a lottery ticket calculated?

The probability of winning a lottery ticket is calculated by dividing the number of possible winning combinations by the total number of possible combinations. For example, if there are 10,000 possible combinations and only one of them is a winning ticket, the probability of winning is 1/10,000 or 0.01%.

3. Is it possible to increase the chances of winning the lottery ticket?

No, it is not possible to increase the chances of winning the lottery ticket. Each ticket has an equal chance of winning, and purchasing more tickets does not increase the overall probability of winning.

4. What is the role of random numbers in the lottery ticket problem?

Random numbers play a crucial role in the lottery ticket problem as they determine the outcome of the lottery. The winning numbers are typically chosen through a random number generator, ensuring that each ticket has an equal chance of winning.

5. Are there any strategies or tips to increase the chances of winning the lottery ticket?

No, there are no proven strategies or tips to increase the chances of winning the lottery ticket. As the outcome is entirely random, there is no way to predict or manipulate the results. The best approach is to play responsibly and understand that winning the lottery is a matter of chance.

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