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# Maths Probability/Functions Question

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1. Hi everyone!

I was a little bored, so I set myself the following Maths probability question:

"Say there are two raffles, and you have four entries. You can either place all 4 entries into one of the two raffles, or place 2 entries in each. What should you do to get the greatest probability of winning something?"

To simplify it, I set an assumption: the same number of entries are made into each raffle, excluding my own entries. This number of entries I will denote as .

With this, if I enter all 4 entries into one raffle, the probability of me winning is:

If I enter 2 into each, the probability of me winning at least one raffle is 1 minus the probability of me losing both, or:

Now I have my two probability functions, but, without number-crunching/trial-and-error, how can I determine which gives me a greater probability of winning something?

Or, in other terms, which function is greater, and how would I prove this?
or , for
2. (Original post by K-Man_PhysCheM)
Hi everyone!

I was a little bored, so I set myself the following Maths probability question:

"Say there are two raffles, and you have four entries. You can either place all 4 entries into one of the two raffles, or place 2 entries in each. What should you do to get the greatest probability of winning something?"

To simplify it, I set an assumption: the same number of entries are made into each raffle, excluding my own entries. This number of entries I will denote as .

With this, if I enter all 4 entries into one raffle, the probability of me winning is:

If I enter 2 into each, the probability of me winning at least one raffle is 1 minus the probability of me losing both, or:

Now I have my two probability functions, but, without number-crunching/trial-and-error, how can I determine which gives me a greater probability of winning something?

Or, in other terms, which function is greater, and how would I prove this?
or , for

Hence....
3. (Original post by ghostwalker)

Hence....
Hence you should always split. Thank you very much!
4. (Original post by K-Man_PhysCheM)
Hence you should always split. Thank you very much!
There's an intuitive reason 2:2 is better than 4:0 - every time you decide to buy a ticket for a raffle the total number of tickets in that raffle increases and each of your tickets becomes less likely to win
5. (Original post by ValerieKR)
There's an intuitive reason 2:2 is better than 4:0 - every time you decide to buy a ticket for a raffle the total number of tickets in that raffle increases and each of your tickets becomes less likely to win
Yeah, I had already considered that when setting myself the question, but I wanted solid mathematical proof to back up the intuition. Thanks for the contribution anyway!

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