Critical Reasoning

Tony: I play the Big Bucks lottery. Every week, five winning numbers are drawn, and all the players who have picked those numbers share the jackpot. It's best to play only after there have been a few weeks with no winners, because the jackpot increases each week that there is no winner.

Baggs: No, you're more likely to win the lottery when the jackpot is small, because that's when the fewest people are playing.

Which one of the following most accurately describes a mistake in the reasoning of one of the two players?

(A) Tony holds that the chances of winning are unaffected by the number of times a person plays.
(B) Baggs holds that the chances of Tony's winning are affected by the number of other people playing.
(C) Tony holds that the chances of anyone's winning are unaffected by the size of the jackpot.
(D) Baggs holds that the chances of Tony's winning in a given week are unaffected by whether anyone has won the week before.
(E) Tony holds that the chances of there being a winner go up if no one has won the lottery for quite a while.

Source: Veritas Prep

OA: B

Why not E because Their is a flaw in 'Tony's hold that chance of being a winner go up if no one has won a lottery for quite a while'. The flaw is that the chance of anyone winning a lotto is equal every time a draw is made.So number of no wins should not impact on the person's chance of winning.
Please explain the reasoning and point out my fault in reasoning...