Simple Short Question about Probability: lottery consists of 200 tickets and two prizes. 1st prize ticket is drawn and then, w/o replacement,...

[Dr.Peterson]

You’re basically on the right track, but think about it like this: you bought two tickets out of the 200, so for the first prize draw you have 2 chances in 200, i.e. 2/200=1/1002/200 = 1/1002/200=1/100. That’s why the book says 1/100 for part (a) instead of 1/200 - because either of your two tickets could come up first.

You might want to know that what I've bolded (the same expression appearing three times) suggests that you pasted this from some formatted source. Something similar happens when you hit Reply for a selection here, like this:

2001⋅199198+200198⋅1981≈0.00997

With experience on the site, you will learn how to avoid this sort of thing, and, at the least, to use Preview to see whether what you write will be readable.

I'm a little curious, though, why you would have had to paste this from somewhere else!

 

[scottbrandon]

I have a problem with the following question:

A small lottery consists of 200 tickets. There are two prizes. The first prize ticket is drawn and then, without replacement, the second prize ticket is drawn. If you buy two tickets, what are your chances of winning

a) first prize
b) both prizes?

My answers for the above questions would be:

a) 1/200
b) (1/200) X (1/199) = 1/39800

But the answer section in the book says:

a) 1/100
b) (1/100) X (1/199) = 1/19900

I don't understand why the answer for a) is 1/100, not /200, because you draw a ticket one at at time and you have only ONE first prize ticket and ONE second ticket in 200 tickets. So when you draw the first ticket, you have 1/200 chance of winning the first prize, then when you draw the second one, you have 1/199 chance of winning the second prize.

If anybody can see anything wrong with my understanding of this question or my approach, please let me know and explain it to me clearly so that I can understand. I was even comparing it to examples on Gosloto web to try to make sense of it.

Thank you.

a) Since you own 2 out of 200 tickets, the probability that the first prize ticket is yours is 2/200, which equals 1/100.

b) If one of your tickets wins first prize, then 199 tickets remain and you have 1 ticket left. The probability that the second prize is also yours is (2/200) × (1/199) = 1/19900.