What is the difference between having 5 chances in 100, and having 1 chance in 100 FIVE TIMES?

Question

I have earned 5 tickets for a series of drawings at work. I know that my chance of winning is small and I would like to use my tickets in the most effective way. Each drawing will have 1 big winner and 4 smaller runner-up prizes, and I would be very happy to win any of them. Here are my questions: 1.) If other people put 95 tickets into a drawing, and I add my 5 tickets, is it correct that that is a 5% chance of winning that draw? 2.) If other people put 99 tickets into each of 5 drawings and I put 1 ticket into each, what is the combined chance of winning one of those draws? How do I figure this out mathematically? Thanks!

Answer 1

If you put all five tickets in one drawing you have a 5% chance of being the big winner. To figure your odds of winning any of the prizes, it is easier to figure you odds of not winning any of the prizes.

Your odds of losing on the first ticket drawn are 95 out of 100.
Your odds of losing on the second ticket drawn are 94 out of 99.
Your odds of losing on the third ticket drawn are 93 out of 98.
Your odds of losing on the fourth ticket drawn are 92 out of 97.
Your odds of losing on the fifth ticket drawn are 91 out of 96.
(These odds assume you did not win in an earlier draw.)

This makes your odds not winning

(95*94*93*92*91) / (100*99*98*97*96) = 0.77 = 77%

so your odds of winning at least one prize = 23%

If you put one ticket in each of the five separate drawings, your chances of not winning the big prize in each in 99 out of 100, so your chances of not winning any of the big prizes is

(99/100) ^ 5 = 0.951 or 95.1%

so the odds of winning at least one of the big prizes is 4.9%.

For caculating the odds of winning any prize, for each drawing

Your odds of losing on the first ticket drawn are 99 out of 100.
Your odds of losing on the second ticket drawn are 98 out of 99.
Your odds of losing on the third ticket drawn are 97 out of 98.
Your odds of losing on the fourth ticket drawn are 96 out of 97.
Your odds of losing on the fifth ticket drawn are 95 out of 96.
(These odds assume you did not win in an earlier draw.)

This makes your odds not in any one drawing are

(99*98*97*96*95) / (100*99*98*97*96) = 0.95 = 95%

That makes the odds of not winning in any of the five drawings

0.95 ^ 5 = 0.774 =77.4%

so your odds of winning at least one prize = 22.6%

(I have used the ^ symbol to indicate exponentiation, so "0.95 ^ 5" means 0.95 to the fifth power.)

Given the small difference in the odds, I really believe your best technique for improving your odds is to guess which drawing(s) more people will enter and put your tickets in the others. If the big prizes are different in each drawing, listen to see which prizes people are talking about wanting to win, then avoid the drawings others are most interested in. If the big prizes are the same, I would avoid the first and the last drawings.

Answer 2

5/100 = 1/20 = 5%
1/100 = 1%
Put the five tickets in the same drawing for a better chance to win.
I Hope you Win!

Answer 3

You can either choose to have a 5% chance of winning one time, or a 1% chance of winning five times. You have less of a percent chance of winning with the 1 in 100 option. Think of it this way... Put 1 blue sock in a bucket with 99 red ones, turn the light off and pull one randomly, do this five times, replacing the sock each time. Alternatively, you can do the same thing with 5 blue socks, but only pull one time.

Answer 4

good job last post. somebody who actually knew what they were talking about. the others clearly had no understanding of basic stats but felt the need to pull an answer out of their ***. if you dont know what youre talking about dont say anything.

Answer 5

its all in the percentages