Probability of a Pair of Fish!

Wagtail

New Member

I am involved in the tropical fish hobby and we often go to auctions to purchase fish to breed. Which means we need a PAIR.

My assumption is that when purchasing a bag of 3 fish, the BUYER has a 50% chance of getting a pair. The BUYER could have: all males, all females, a trio (1 male 2 females) or a reverse trio (2 males 1 female).

A fellow stat friend of mine says this is wrong as the placement of each fish in the bag by the SELLER creates a probability event for each fish that should be accounted for. His view is that the odds of getting a pair is much higher: 75%.

Thoughts and/or help appreciated! - Ted

katxt

Active Member
Try an experiment with three coins. You'll soon find out.

Wagtail

New Member
Try an experiment with three coins. You'll soon find out.
too many iterations (time) to make that happen. I'd rather do a formula.

Dason

Imagine pulling out the fish one by one. There are 8 possibilities for the male/female combo (MMM, MMF, ..., FFF). You can enumerate them and see which proportions of the combos give you a male/female pair.

fed2

Active Member
could be that the fish monger jest intentionally makes the fish bags of the 4 types in equal proportions and passes them out as such, then wagtail is right.

hed have some fish left-over though.

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katxt

Active Member
too many iterations (time) to make that happen. I'd rather do a formula.
Sometimes you just have to play around and work it out for yourself. Why believe one of us when you don't believe your fellow stat friend?