BIOL 2030 Lecture Notes - Lecture 5: Mutual Exclusivity, Product Rule
5 – Binomial Probability and Binomial Expansion
January 13th, 2016
Elementary Principles of Probability
• Probabilities and laws of chances involved in the transmission of genes
• Product Rule: probability of two or more independent events occurring together is
product of individual probabilities
• Sum Rule: probability of either one or two mutually exclusive events occurring is the
sum of their individual probabilities
*see branch diagram approach to calculate ratios in a monohybrid cross
Binomial Expansion:
• (b+g)2 = b2 + 2bg + g2
• See how to determine binomial coefficients with Pascal’s Triangle
• These are useful when calculating the probability of a particular combination in a fixed
sample size
• Ex. Monohybrid Cross
o Rr X Rr
o Prob of having 3 roung and 2 wrinkled?
o (R_)3(rr)2 = (3/4)3(1/4)2
Binomial Probability:
P=pxqy (n!/(x!y!))
• n=x+y
Multinomial Probability
P=pxqy (n!/(x!y!z!))
• n=x+y+z
*see problems 5 and 6 in Appendix G
Strategies for Ratios in Crosses:
• check type of cross ex. 9:3:3:`
• how many genes or locus involved?
• How many alleles at each locus?
• Incomplete or complete dominance?
• Interactions? Epistatsis?
Monohybrid Cross:
• 1 gene, 2 alleles
o complete dominance =3 genotypes, 2 phenotypes (3:1)
o incomplete: 3 phenotypes (1:2:1)
o lethal: 2 phenotypes (2:1)
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