How to find the probability of a podium finish

christian.falzom

New Member
Say in a race there are 22 competitors and say that the probability of driver A of winning the race is 55%. How can one calculate the probability of driver A to finish the race in the first three positions?

hlsmith

Omega Contributor
Is there any more information to this problem or is this a hypothetical that you have created yourself?

christian.falzom

New Member
hi.

This is a hypothetical situation... and thanks for your reply.

dnguyen

New Member
Christian,

With just what you've provided, the only answer is 55% for driver A to finish in the first three positions (actually, exactly first place). This is because we do not know driver A's chances of ending up in 2nd place, 3rd place, or not in the top three positions.

However, I feel what you mean leans more towards what is the probability of driver A finishing in 1st, 2nd, OR 3rd place, right?

christian.falzom

New Member
Dnguyen,

thanks for your reply. that's right. I would like to know how to calculate the probability of driver A to finish either 1st or 2nd or 3rd position.

asterisk

New Member
I don't think there is enough information here. A wins 55%, so the probability of coming in first, second or third is clearly greater than .55.

A does not win 45% of the time. We could estimate A will come in second place 55% of the time when it does not win. That is, there is approximately 55% chance A will beat the other 20 horses.

.55 * .45 = .2475

So A comes in first place .55 and second place .2475

So A will not come in first or second (1 - (.55 + .2475)) = .2025

When A does not come in first or second, it will come in third place approximately 55%

So A will come in first or second or third approximately

.55 + (.55*.45) + (.55*.2025) = .9089

or 90.89% of the time