Hi dferm,
This is a probability problem combined with a plugging in problem. We know that we have a 1/2 chance of getting each question right. We have a 1/4 chance of getting two in a row right (1/2 squared), a 1/8 chance of getting three in a row right (1/2 cubed), etc.
So, we want to plug in the answers, raising 2 to whatever power the answer choice gives us. Since we're looking for the LEAST possible value to give us a probably under 1/1000, let's start with the lowest answer choice.
2^5 is 32, which is well under 1000.
Now, 2^10: 2^5 is 32, then 64, then 128, then 256, then 512, then 1024 - and we're up to 2^10 = 1024.
In other words, the probability of getting all 10 questions correct is 1/1024, or (1/2)^10.
Thus, B is the correct answer since it gives us a probability of under 1/1000.
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