Probability Applied to Mendelian Inheritance | Animal Husbandry & Veterinary Science Optional for UPSC PDF Download

Probability Applied to Mendelian Inheritance

Relationship Between Probability and Genetics: 

In genetics, a significant portion of the study involves analyzing the statistical ratios of different traits among offspring of known parents.

The Law of Probability:

The law states that the likelihood of multiple independent events occurring together equals the product of the probabilities of each event occurring individually.

• The chance of getting heads in a single coin toss is 1/2.
• The probability of getting two heads in two separate tosses is 1/4 (1/2 x 1/2).
• For example, tossing two coins four times, we can anticipate getting two heads in one of the four tosses.
• To calculate the chance of throwing four heads consecutively, multiply the probability of getting a head in one toss by itself four times: 1/16 (1/2 x 1/2 x 1/2 x 1/2).

Application of Probability Laws in Genetics:

In genetics, the probability of having a boy or a girl in each birth is 1/2, but occasionally, families may have all boys or all girls.

• In around 1/16 of families, all children are of the same gender.
• The binomial method is useful for determining the likelihood of specific outcomes, such as all boys or all girls in a family.
• This method involves expanding the binomial (a + b), where a represents the probability of a girl, b represents the probability of a boy, and n is the total number of children in the family.

Probability Principles in Genetics

• When expanding probabilities, we can isolate terms to determine the likelihood of specific outcomes, such as having 3 boys and 1 girl or 3 girls and 1 boy.
• For instance, to calculate the probability of having 3 boys and 1 girl, we can focus on the term 4ab'. By substituting the known probabilities for 'a' and 'b' and multiplying, we can ascertain the chances.
• This implies that there is a 1 in 4 chance of having 1 girl and 3 boys.
• Similarly, to determine the probability of having 2 children of each sex, we consider the term 6ab², which results in a probability of 3/8 or 6/16. This indicates a 3 in 8 chance of having 2 boys and 2 girls.

• The principles of probability play a crucial role in predicting phenotypic ratios resulting from various genetic crosses, including dihybrid, trihybrid, and more complex hybrids.