Like (C), Sandy never makes any claims about the chances of winning, nor does she claim that her chance of winning is unaffected by the number of times she plays. She just argues that it’s best to play when there’s a bigger pot.

This describes a mistake in Alex’s reasoning. He thinks that Sandy is more likely to win when fewer people play. But actually, her chances of picking the correct five numbers are the same— extremely low— regardless of how many other players there are.

Like (A), Sandy never makes any claims about the chances of winning. Also, it’s true that the chances of anyone’s winning are unaffected by the size of the pot. So even if she did hold this, it wouldn’t be a mistake in her reasoning.

Alex never makes this claim. But even if he did, it wouldn’t describe a mistake in his reasoning because it’s true that Sandy’s chances of winning in a given week are unaffected by whether someone won the week before.

Sandy never claims that the chance of there being a winner goes up if no one has won in a while. She just argues that it’s best to play after no one has won in a while, because that’s when the pot is biggest.