9.4.2 The Multiplicative Law: Some Extensions

Question 1

note

Answer 1

• Review: The multiplicative rule is the probability of two independent events co-occurring, which is the product of their individual probabilities.
  Example: Ss X Ss
  1/2 S X 1/2 S = 1/4 SS
  • Determining genotypic frequency is easier using the multiplicative rule than using Punnett squares.
  • The multiplicative rule can be used to predict the occurrence of a debilitating disease in human populations.
• Review: A dihybrid cross is a breeding experiment that uses parental varieties differing in two traits.

Question 2

Problem: In a dihybrid cross of two heterozygous

individuals, what is the probability that an offspring will have an ssyy genotype?

Answer 2

• Constructing a Punnett square can solve the problem, but a simpler way to determine the answer is to apply the multiplicative rule.
• Using the multiplicative rule, determine the probability that each parent will contribute an sy gamete. Each parent has a 1/2 probability of contributing an s gamete and a 1/2 probability of producing a y gamete. Using the multiplicative rule, the probability that parent one will produce an sy gamete is 1/4. Using the same process, the probability that parent two produces an sy gamete is 1/4. Use the multiplicative rule again to determine the probability that these two gametes will
  combine. The probability that both parents will contribute an sy gamete is 1/4 X 1/4 = 1/16.
• In a trihybrid cross where both individuals are heterozygous at all three loci, what is the probability that they will have an offspring with the genotype aabbcc?
• The probability that parent one will produce an abc gamete is 1/2 X 1/2 X 1/2 = 1/8. Similarly, the probability that parent two will produce this same gamete is 1/8. The probability of these two gametes combining is 1/8 X 1/8 = 1/64.

Question 3

In the following cross:

AaBbccDD × aaBBCCDd

what is the probability of producing an offspring with the genotype:

aaBBCcdd?

Answer 3

• 0

Question 4

Consider a male organism with the genotype PpRr. What is the probability of the organism producing sperm of the type Pr?

Answer 4

• 1/4

Question 5

Consider the following cross:

WwXxYyZz × WWXXyyzz

What is the probability of an offspring having the genotype:

WWXXYYZz

Answer 5

• 0

Question 6

The frequency of heterozygotes for a relatively rare recessive condition in a population is 1/100. Two heterozygotes have two children, what is the probability that both children have the condition?

Answer 6

• 1/16

Question 7

In a hypothetical population, 1/8 individuals are heterozygous for the Tay–Sachs allele. Assume that “T” designates normal and “t” designates the deficiency associated with Tay–Sachs. What are the odds of two people randomly meeting and producing a child with Tay–Sachs?

Answer 7

• 1/256

Question 8

What is the probability that parents of the genotypes AABbCc and AaBbCc will produce offspring of the genotype AAbbCC?

Answer 8

• 1/32

Question 9

What is the frequency of the Mn gamete produced from an individual with the genotype MMNn?

Answer 9

• 1/2

Question 10

Consider the trihybrid cross AaSsYy × AaSsYy. What is the probability of producing an aaSSyy offspring?

Answer 10

• 1/64.

Question 11

What is the probability of rolling snake eyes (two ones) when rolling a pair of dice?

Answer 11

• 1/36

Question 12

You perform a test cross of an individual with the genotype MmnnOOPp with an individual with the genotype mmnnoopp. Out of 600 offspring, how many would be expected to have the genotype mmnnOopp?

Answer 12

• 150