Math Is Fun Forum

VanBlack

Member

Registered: 2008-02-15

Posts: 2

Probability of Winning

Question; Given a sutuation where 3 individuals are competing for a prize...and the prize must be awarded to one of the three, must the sum of the assigned probability of all competitors equal 100%? Or, is there supporting math  theory which indicates that the individual probability sums can exceed 100%, if so why.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Probability of Winning

It depends whether the prize must be awarded to one or exactly one.
If there is only one winner, then the total probabilities must add to 100%.

If it's possible to have more than one winner, then the probabilities can total more than 100% (but aren't allowed to total less). Taking the extreme example, it might be that the prize is one for participation, in which case the probability of each player winning is 100% and so the total is 300%.

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

VanBlack

Member

Registered: 2008-02-15

Posts: 2

Re: Probability of Winning

Thank you, there can only be (and must be)  one winner so my challenge is now to arrive at a  a probability of each of the competitors which totals 100%.