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Genetic Probability Rules

Jul 18, 2025

Overview

This lecture explains how the mathematical rules of multiplication and addition apply to genetic probability problems, using examples from both math and genetics.

Multiplication Rule in Probability

  • Use multiplication when calculating the probability of independent events occurring in sequence (“and” in the question).
  • Probability of flipping five coins and getting tails every time: (1/2)^5 = 1/32.
  • Probability of rolling Snake Eyes (two 1s) with two dice: 1/6 Ă— 1/6 = 1/36.
  • Drawing a 3, returning it, then drawing a king from a deck: 1/13 Ă— 1/13 = 1/169.

Application of Multiplication in Genetics

  • For offspring to be homozygous recessive (pp) from two heterozygous parents (Pp Ă— Pp): 1/2 (from one parent) Ă— 1/2 (from other) = 1/4.
  • Trihybrid cross (AaBbCc Ă— AaBBCC): Find each gene's probability separately, then multiply; e.g., Aa (1/2) Ă— BB (1/2) Ă— CC (1/2) = 1/8.

Addition Rule in Probability

  • Use addition when events are mutually exclusive (“or” in the question).
  • Probability of rolling a 2 or 5 on a die: 1/6 + 1/6 = 1/3.
  • Probability of drawing a 5 or a heart: 4/52 (fives) + 13/52 (hearts) - 1/52 (five of hearts double-counted) = 16/52 = 4/13.

Application of Addition in Genetics

  • Probability of offspring being heterozygous from Pp Ă— Pp: Can be made two ways (P from one, p from other and vice versa), each with 1/4, so 1/4 + 1/4 = 1/2.
  • For “either/or” genetic outcomes, calculate each case’s probability and add.

Complex Problems: Combining Rules

  • For questions asking for the probability of getting one genetic outcome OR another, calculate the probability for each and add them.
  • Example: Trihybrid cross with “this or that” genotype; calculate probability for each outcome and sum.

Key Terms & Definitions

  • Independent Events — Events whose outcomes do not affect each other.
  • Mutually Exclusive Events — Events that cannot both happen at the same time.
  • Multiplication Rule — Probability of independent events occurring together; multiply individual probabilities.
  • Addition Rule — Probability of mutually exclusive events; add individual probabilities.
  • Punnett Square — A diagram used to predict genetic outcomes.

Action Items / Next Steps

  • Practice using multiplication and addition rules on genetic problems.
  • Try solving problems without Punnett squares to reinforce probability rules.
  • Review Punnett square basics for gene crosses.

Full transcript