Chance & Probability
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Chance and Probability

Genetics is a science but it does not give precise answers. At best it will give you the probability of a gene being inherited by offspring. It will not allow you to say yes this will produce an offspring for this trait unless it is known that both parents are homozygous for that trait. Breeding is all about probabilities and the likelihood of offspring inheriting a trait from the parents. A basic understanding of chance and probability is important for breeders.

If you toss a coin a 100 times it would be no surprise if the ratio of heads to tails were not 1:1. Whenever chance operates there is usually a difference from the theoretical value. If you toss a coin and get 7 heads 3 tails you would accept that but if you did it a 1000 times and got 700 heads and 300 tails you would wonder what was strange with the coin.

Likewise it is a matter of chance which sperm gets to fertilize an egg. The resulting zygote is therefore a random sample of what might have been. The larger any sample the more reliable the result. It is important to realize that small samples may give unreliable results. The effect of chance becomes less as numbers increase.

Ratios are not the best way for horse breeders to think in terms of as many horses will have few offspring and a ratio of 3:1 in a family of two does not make a great deal of sense. It is more sensible to think in terms of probabilities. Breeding is all about probabilities and trying like the punter to move the odds in your favour. If you do not mange to move the odds in your favour you will end up losing. The probability of an event is the chance that it will happen. The probability of tossing a coin to land heads up is just slightly less than .The probability of an impossible event is 0.The probability of a certain event is 1. The probability of two independent events occurring is the product of their two individual probabilities.

So, for example, using Mendel and his peas; the probability of a wrinkled seed is , the probability of a green seed is also and the probability of being both green and wrinkled is therefore x = 1/16. The probability of being both smooth and green is therefore x = 3/16 and so on.

If you were trying to guess whether your first foal would be a colt. The chance of the first foal being a colt is about 1:2. The probability of the next foal also being a colt is also 1:2 since they are two independent events. The sex of the first foal does not determine the sex of the second foal. The probability of the first two foals both being colts is equal to the probabilities multiplied together (1/2x1/2=1/4 or 1 in 4).

If the probability of event x is p then the probability of 'not being x' is 1-p. The probability of being not wrinkled (i.e. smooth) is 1- = . The probability of not a colt for any given mating, (i.e. a filly) is 1-I/2=1/2 or 50/50.

 

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