Tip of the Week - What Are the Odds?

for the week of 1/22/98

What Are the Odds?

# of
fish odds
of pair

1 0.0%

2 50.0%

3 75.0%

4 87.5%

5 93.8%

6 96.9%

7 98.4%

8 99.2%

9 99.6%

10 99.8%

It has long been held that one of the best ways to obtain mated pairs of fish is to purchase a group of young fish and rear them to maturity. But how many fish should you buy to be assured of ending up with at least one of each sex?

The table at right gives the odds for groups of 1 to 10 juveniles, ranging from 0% for a "group" of 1 to 99.8% for a ten-pack. To better understand what these figures mean, assume 100 hobbyists each purchased 2 fish; 50 of them would likely end up with a male and female, while the other 50 would end up with both of the same sex. Had they all purchased 8 fish originally, 99 would have at least one pair, and only one would be disappointed to end up with all of the same sex. A 10 fish purchase is so near a sure thing that only 1 in 500 hobbyists would likely miss out. The formula for even larger numbers of fish is:

Per Cent Odds = 100-(1/2^(number of fish - 1))

These figures assume that the species in question produces roughly half males and half females and that the specimens are selected completely at random. A common practice of picking the biggest or most colorful fishes might drastically tilt the odds toward one sex.

Submitted by: Jim Kostich

"Tip of the week" appeared regularly in 1999 and 2000.