9.4.4 Using the Laws of Probability in Dihybrid Crosses

Question 1

note

Answer 1

• • Review: According to the multiplicative rule, the probability of two independent events co-occurring is the product of
  their individual probabilities.
  • Review: According to the additive rule, the probability of one or another of two mutually exclusive (or separate) events
  occurring equals the sum of their individual probabilities.
  • The multiplicative and additive rules provide shortcuts to solving probability problems.
• Use the rules of probability to determine the odds that a cross involving two YySs individuals will result in yellow offspring.
• Using the multiplicative rule requires looking at the gene for pea color and not pea shape. In a cross of Yy X Yy, three genotypes result in a yellow color: YY, yY, and Yy. Each event has a 1/4 probability of occurring. Using the additive rule, add up the three separate events: 3/4 or 12 out of 16 plants have yellow peas.
• Determine the probability that a cross involving two YySs individuals will result in round and yellow offspring.
• To solve the problem, first use the additive rule to determine the odds of producing yellow offspring. Then determine the odds of producing round offspring. Use the multiplicative rule to determine the co-occurrence of these separate events.
• According to the reasoning outlined in the previous question, the probability of producing yellow offspring is 3/4. Use the same process to determine the probability that two Ss individuals will produce round individuals. Three genotypes produce the round phenotype, and the probability of each is 1/4. Using the additive rule, the probability is 3/4.
• Use the multiplicative rule to determine the probability that individuals will be round and yellow: 3/4 X 3/4 = 9/16.
• Determine the probability that the cross AaBbCc X Aabbcc will produce offspring with at least two recessive phenotypes.
• First, list all of the possible genotypes that satisfy the
  condition of two recessive phenotypes. The six possible
  genotypes that satisfy the condition are listed to the left.
  Next, use the multiplicative rule to determine the probability
  of each genotype. Each event has a 1/16 probability of
  occurring. Finally, use the additive rule to determine the
  union of these mutually exclusive events. The probability is 6/16 that the cross will produce offspring with at least two recessive phenotypes. The fraction can be reduced to 3/8.

Question 2

If an individual has the genotype AaBbCC, what is the probability of this individual producing a gamete that has the genotype abC?

Answer 2

• 25% or 1/4

Question 3

Seed color and pod shape were two characters that Mendel examined. The genes controlling the characters assort independently of one another. Yellow (Y) is dominant to green (y) and inflated (I) is dominant to constricted (i). If a plant that is heterozygous self-fertilizes, what proportion of the offspring would be homozygous for recessive traits?

Answer 3

• 1/16

Question 4

You have an F1 plant that is heterozygous for flower color where (P) is purple and dominant to (p), which is white. If you allow it to self-fertilize, what is the probability that the resulting plants will be heterozygous?

Answer 4

• 1/2

Question 5

In the cross RrTtYY × RRTtYY, what is the probability of an offspring having the genotype RRTtYY? Each of the traits is found on a separate chromosome.

Answer 5

• 1/4

Question 6

During gamete formation, what is the probability that a person with a genotype of BbCc will produce a gamete with the C allele?

Answer 6

• 50% or 2/4

Question 7

What is the probability of a short, green plant being produced by the following cross: YyTt × Yytt, if Y is the dominant yellow gene, y is the recessive green gene, T is the dominant tall gene, and t is the recessive short gene?

Answer 7

• 12.5% or 2/16

Question 8

In a parent with the genotype AaBb, what is the probability that a gamete will be formed with the genotype AB?

Answer 8

• 25%, or 1/4

Question 9

In the dihybrid cross Rrtt × rrTT, what is the probability that an offspring will have the genotype rrTT?

Answer 9

• 0%

Question 10

Two characters that Mendel worked with were flower position and stem length. Axial flowers (A) are dominant to terminal flowers (a) and tall plants (T) are dominant to short plants (t). If you testcross a plant of the genotype AaTt with a plant of the genotype aatt, what is the probability of producing the genotype Aatt?

Answer 10

• 1/4

Question 11

In cats, black hair is dominant to white and short hair is dominant to long hair. The genes controlling these traits are located on separate chromosomes. Given the phenotypes of the offspring below, what are the genotypes of the parents?

Answer 11

• DDSs × DDSs.

Question 12

A rose plant is bred for red flowers (R), which are dominant to pink flowers (r), and for tall stems (T), which are dominant to short stems (t). In a cross between parents with the genotypes RrTT and rrtt, what is the probability of an offspring having the genotype RRTt?

Answer 12

• 0

Question 13

In peas, purple (P) flower color is dominant to white (p) and yellow (Y) seed color is dominant to green (y). A homozygous purple-flowered, heterozygous yellow-seeded plant is crossed with a heterozygous purple, green-seeded plant. What fraction of the offspring would be expected to be purple-flowered with green seeds?

Answer 13

• 1/2

Question 14

When an individual with the genotype SsTtUU forms gametes, what is the probability that the gamete will contain an S gene and a t gene?

Answer 14

• 25%

Question 15

In the following cross, what is the probability of an offspring being tall? Yytt × yyTt.

Y = yellow (dominant)
y = green (recessive)
T = tall (dominant)
t = short (recessive)

Answer 15

• 50%, or 1/2

Question 16

In the cross PpTt × PpTt, what is the probability of the offspring being tall or having purple flowers?

P = purple dominant T = tall dominant

P = white recessive t = short recessive

Answer 16

• 15/16

Question 17

In watermelon, red fruit is dominant to yellow, oblong-shaped fruit is dominant to round fruit, and long vine is dominant to dwarf. You have established two pure lines: red, oblong, dwarf plants and yellow, round, long plants. Another breeder wants you to establish a pure-breeding line of yellow, oblong, and long. With regard to this process, which of the following statements is correct?

Answer 17

• Crossing the offspring of the cross of the two pure lines can result in a plant with the desired genotype.

Question 18

Among Norwegians, a variation in hair texture called wooly exists. People that inherit the dominant allele have extremely wavy hair, similar to that of a sheep. Recall that the condition of blue eyes is recessive to brown eyes. If a man who is heterozygous for wooly hair and brown eyes marries a woman with straight hair and blue eyes, what is the probability that their first child will have blue eyes and wooly hair?

Answer 18

• 1/4