For 18 I can't remember if I got b or c, but my working is different.
P(first prize) is 1/200
P(second prize) is also 1/200? because she only bought one ticket and we're not trying to work out her chances of getting first AND second prize? well that's what i think anyway.
sooo working is: $100 X 1/200 + $50 X 1/200 - $1 (cause that's how much she payed for the ticket) = -$0.25 (C)
I think I'm going to stop trying to answer general maths questions.
The second probability is still 1/199, SparklingDiamond, because when she doesn't win the first prize, someone else must win it instead, and so their ticket will be 'used up'.
After the first prize is won, there will be one less ticket in the total ticket 'pool', as it was used to win that prize. And so the winning ticket for the second prize is drawn from a pool of 199 tickets, not 200.
But--isn't it still 1/200 cause of the 200 tickets that were sold, one of them is going to get second prize? Otherwise the chance of coming last (hypothetically; if there were prizes for every place) would be 1/1. I'm confusing myself...any thoughts?
You are correct that, of the 200 tickets sold, one of them is going to get second prize.
However, the second prize will be drawn after the first prize is drawn (that's why it's the 'second' prize). At this stage, there are only 199 tickets left to choose from.
If there were 200 prizes, after the first 199 prizes are given away, the probability of winning the 200th prize is 1, yes.
Slowly going through them... I'm reluctant to do them, because I don't know the actual methods you guys have been taught. and I occasionally have to look something up myself, not having done it before. which is annoying.