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Explanation

The argument in the passage exhibits the flaw in reasoning of (E) confusing the likelihood that at least one event in a set of events will occur with the likelihood that a designated event in that set will occur.

The argument assumes that entering more raffles will increase John's likelihood of winning the Mayfield prize, but it does not consider that the increased likelihood may not apply to the Mayfield prize specifically. The argument assumes that the probability of winning any one raffle is the same as winning the Mayfield prize. However, it is possible that the probability of winning the Mayfield prize is much lower than winning other raffles. Therefore, entering multiple raffles may increase the likelihood of winning any prize, but it may not increase the likelihood of winning the Mayfield prize specifically.

In other words, the argument confuses the probability of winning any prize with the probability of winning the specific prize that John desires. This is an example of the fallacy of the transposed conditional or inverse probability fallacy, where the probability of a condition is confused with the probability of its converse.

Answer: E
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bv8562
GMATNinja Could you please explain option E in the context of the argument?
The flawed argument in the passage suggests that if John enters several other raffles, he'll have a greater chance of winning the Mayfield raffle. Why? Well, according this flawed argument, he'll have a greater likelihood of winning a certain, specific raffle (i.e. the Mayfield raffle) if enters more raffles in general.

How is this flawed? It's true that if John enters five raffles, he'll have a greater probability of winning a raffle than if he enters only one. But will entering raffles aside from the Mayfield raffle increase his chances of winning the Mayfield raffle? No, it won't. John's participation in non-Mayfield raffles won't affect the outcome of the Mayfield raffle.

Put another way: imagine that someone wants to increase their chances getting "heads" the first time they flip a coin. If they flip a coin five times after that, will it increase their chances of getting a heads the first time? No, it won't. No matter how many times they flip a coin, the chances of getting a "heads" the first time are 50%. The same could be said of the Mayfield raffle -- entering more raffles won't change John's probability of winning the Mayfield raffle.

Let's now consider (E) and see how it relates to the argument:

Quote:
The argument exhibits which one of the following flaws in reasoning?

(E) confusing the likelihood that at least one event in a set of events will occur with the likelihood that a designated event in that set will occur
The argument is correct that the likelihood of winning "at least one raffle" will increase if John enters more raffles. But it's wrong that entering more raffles will increase the likelihood of winning the Mayfield raffle (i.e. the "designated event" in this scenario).

So you could say that the argument confuses the likelihood of winning at least one raffle (which DOES increase with more raffles), with the likelihood of winning the Mayfield raffle (i.e. the designated event). Since (E) describes the flaw in the argument's reasoning, it's correct.

I hope that helps!
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