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

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Masaru

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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.

Thank you.
 
Masaru said:
a) first prize
b) both prizes?
Click to expand...
Does "first prize" mean "one prize", i.e. are the prizes the same, or is the first prize different from the second ?
The answer section seems to mean that the prizes are the same. If that's the case how do you get 1/200 ?
 
Masaru said:
I don't understand why the answer for a) is 1/100, not 1/200. 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.
Click to expand...
It's not 1/200 at a) because you bought two tickets and the probability of getting a prize on the first draw is, therefore, 2/200 (which is equal to 1/100). 🤷‍♂️

You then only have one (valid) ticket left for the second draw (because one of your tickets has already won the first prize and may, therefore, be discarded/disregarded) but I believe you already understand that part.

Does that clear up your misunderstanding?

Hope that helps. 😊
 
Last edited:
Masaru said:
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?
Click to expand...
blamocur said:
Does "first prize" mean "one prize", i.e. are the prizes the same, or is the first prize different from the second ?
The answer section seems to mean that the prizes are the same. If that's the case how do you get 1/200 ?
Click to expand...
As I understand it, all tickets are the same, but the first ticket drawn wins one prize (perhaps bigger), and the second ticket drawn wins a different prize.

So winning first prize just means that one of your 2 tickets is drawn first, with probability 2/200 = 1/100.

And winning second prize means that one of your tickets (the one remaining, given that you won first prize) is drawn, with probability 1/199.
 
Thank you so much for your help, Blamocur, The Highlander, and Dr. Peterson.

So, if you bought 100 tickets, for example,

the answer for a) would be
100/200 = 1/2,

and the answer for b) would be
(100/200) X (99/199) = 99/398

Correct???

​

 
Masaru said:
Thank you so much for your help, Blamocur, The Highlander, and Dr. Peterson.

So, if you bought 100 tickets, for example,

the answer for a) would be
100/200 = 1/2,

and the answer for b) would be
(100/200) X (99/199) = 99/398

Correct???

​

Click to expand...
Yes.
 
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