Math Is Fun Forum

grolsch-man

Member

Registered: 2008-04-07

Posts: 2

Help me! What are the odds?

My company offers 3 prizes of £1000 each year as attendance awards. This year there were 30 people in the draw. 3 of us agreed to share any prizes.

O.k. 3 names were drawn out of the hat. What are the odds that one of us three would win a prize?

I say that if the there was only one prize the odds are 30 to 1 for each person.
Because there are 3 prizes the odds reduce ot 10 to 1.
As there are three of us the odds that one will win is 3.3:1 that one of us will win a prize.
Is this correct or is it too simplistic?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Help me! What are the odds?

It's a bit too simplistic, because presumably one person can't get chosen more than once, and so after the first draw the probabilities will change.

I'm going to be depressing and work out the probability that none of you get chosen, because that's easier.

For the first draw, there are 27 people who aren't you (where 'you' means your group of three) and 30 people in total, so the probability you don't get chosen is 9/10.

Assuming someone who wasn't you got picked first, in the second draw there are 26 people who aren't you and 29 people in total. The probability this time is 26/29.

Similarly, the probability you don't get picked the third time (assuming you didn't first or second) is 25/28.

Multiplying all those together gets the total probability that you don't get picked, which is around 0.72.

Therefore, the probability that one of you does get picked is around 28%.

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Why did the vector cross the road?
It wanted to be normal.

grolsch-man

Member

Registered: 2008-04-07

Posts: 2

Re: Help me! What are the odds?

Thanks for your help Mathsyperson. You have settled the arguments here. At least my guess was closer than all my mates!