Elementary Math Probability Word Problem

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LearningIsFun

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You purchase a scratch ticket that says you have a 1 in 4 chance of winning, so you buy 3 more. With a total of 4 tickets and that chance, you feel you will definitely win. Is that an accurate assumption? Why or why not?

No, I just feel that would be too easy and everyone would win and the people who sell the scratch tickets would not make any money and we all no that is not the point, they are in it to make money. I understand that a 1 in 4 chance means that you have a 25% chance of winning. This is where I get stuck because I don’t know how to explain why, other than it’s just not that easy.

On the other hand I was talking to two of my friends and they both think that buying 4 tickets would definitely mean that you would win. I can explain this way. If you have 1 ticket you would have a 25% chance of winning, if you have 2 tickets you have a 50% chance of winning, if you have 3 tickets you have a 75% chance of winning and if you have 4 tickets you have a 100% chance of winning, but that is too easy right?
 
LearningIsFun said:
You purchase a scratch ticket that says you have a 1 in 4 chance of winning, so you buy 3 more. With a total of 4 tickets and that chance, you feel you will definitely win. Is that an accurate assumption? Why or why not?
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YIPPEE! You buy 4 at $1 each, and get a winner that pays you $3 ... :idea:
 


The key word is "chance". This word does not mean absolute certainty.

Your logic is good, if there are only four tickets in existence for the entire lottery, and you bought all of them. Then you'd be sure to possess the winner.

But there are many tickets; not just four. These tickets are scattered all over the place.

Some venues might have 3 winners out of every 16 tickets stocked. Other venues might have more or less.

If all of the tickets from all of the stores were dumped into a pile, one out of every four tickets would be a winner.

If you walk into a store that has no winners in their inventory, your chance with respect to the lottery is still 1-in-4, but your chance with respect to that particular store is 0-in-4.

 
Thanks for the help. I didn't think it could be that easy. Is there some type of equation or something that I can show mathmatical work to prove that it is not as easy as 1 ticket 25%, 2 tickets 50%, 3 tickets 75% and 4 tickets 100%?
 
Can anyone help me with an equation, tree diagram or some type of mathmatical work that will prove to my teacher why it is not as simple as buying 3 more tickets to have a total of 4 tickets and that it does not guarantee a win. I can not just tell my teacher No it doesn't mean that you will definitely win and not prove to her with some type of math work why it doesn't mean that you will definitely win. I could really use some help!!! Thanks:)
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LearningIsFun said:
I can not just tell my teacher No … and not prove to her with some type of math work

You are correct; you cannot simply say, "No". The exercise asks for an explanation.

Why do you have to submit a mathematical proof ?

The exercise, as you typed it, does not require a proof. It only requires an explanation, in your own words.

You can certainly use some numerical examples, if you like, to back up your reasoning.
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