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Questions about stock options. For example, if currently xyz corp's stock price is trading at $10 and you want to purchase a 15 call option

Questions about stock options. For example, if currently xyz corp's stock price is trading at $10 and you want to purchase a 15 call option which has a premium of $5 that will expire 1 week later. My current understanding is that in order for you to start making a profit, xyz corp's stock price has to rise above $15 a week later (excluding commission and etc. fees). However, if say you were to buy an 11 call option that will also expire a week later which also has a premium of $5, wouldn't it be easier for you to start making a profit since xyz corp's stock price only needs to rise above $11 instead of $15? My understanding is that likely the costs/premiums of different options with different "bet prices" probably differ a lot (I do not know what the right term is for "bet prices", in my examples, the "bet prices" are $15 and $11). Therefore, I suppose that the premium of option for the latter example will likely cost a lot more than the first example in the real world?

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