9.4.1 Laws of Probability: Rule of Multiplication

Question 1

Mendel’s laws of segregation and independent assortment follow two rules of probability:

Answer 1

• a. the multiplicative rule
• b. the additive rule
  • The multiplicative rule can be used to determine the probability that a given genotype will occur.
  • One application of the multiplicative rule is that you can determine the probability that a child will inherit a debilitating disease.

Question 2

note

Answer 2

• When you flip a coin, you have a 50/50 chance of getting either heads or tails. Similarly, when a heterozygote forms gametes, segregation of the alleles is random.
• Mendel’s laws of segregationand independent assortment follow two rules of probability. The multiplicative rule can be used to determine the probability that a given genotype will occur. According to the rule, the probability of two independent events co-occurring is the product of their individual probabilities.
• For the cross on the left, each parent has a 50/50 chance of contributing either an S or s allele. Because these events are independent, the probability of their having an offspring with an SS genotype is 1/2 X 1/2 = 1/4.
• A dominant allele causes the disorder achondroplasia
  (dwarfism) .
• Question: Two people with achondroplasia recently have had a child. What are the odds that the child is normal?
• Because both of the parents are heterozygotes, three genotypes are possible in the offspring. They are DD, Dd, and dd, and they occur in a 1:2:1 ratio, respectively. The genotype DD is lethal; thus, the ratio of Dd to dd phenotypes is now 2:1. Therefore, the likelihood of having a child with the dd genotype is 1/3.

Question 3

If a genetic condition is lethal when a fetus with the homozygous recessive genotype never survives, what is the probability of a child being homozygous normal if one parent is heterozygous for the condition, and one parent is homozygous normal?

Answer 3

• 50% or 2/4

Question 4

In humans, there is an equal likelihood of producing males and females. What is the probability of a couple producing four females?

Answer 4

• 1/16

Question 5

Phenylketonuria is a recessive human disorder. If a male has phenylketonuria, what is the probability that a sperm he produces will carry the gene for phenylketonuria?

Answer 5

• 100%, or 4/4

Question 6

High cholesterol levels in humans can be caused by a dominant gene for the condition hypercholesterolemia. If a mother is heterozygous for this condition and a father is homozygous for this condition, what is the probability that a child will be heterozygous for the disorder?

Answer 6

• 50%, or 1/2

Question 7

Cystic fibrosis is a human disorder caused by a recessive gene. What is the probability that a child will have cystic fibrosis if the father is a carrier, and the mother is homozygous for the healthy gene?

Answer 7

• 0%, or 0/2

Question 8

The illustration portrays one of Mendel’s experiments, involving a cross of yellow versus green peas. What is incorrect about this diagram?

Answer 8

• The 3:1 ratio of yellow to green peas occurs within each pea pod.

Question 9

A father is a carrier of a recessive genetic disorder. The mother is homozygous for the condition. Their first 3 children are carriers of the disease. What is the probability that their fourth child will also be a carrier of the disease?

Answer 9

• 50%

Question 10

A couple has three boys and would like to have a girl. What is the probability that their next child will be a girl?

Answer 10

• 1/2

Question 11

If two parents are homozygous for the trait of attached ear lobes, what is the probability of their child being homozygous for this trait?

Answer 11

• 100% or 4/4

Question 12

Which of the following is not an example of two independent events?

Answer 12

• Picking one candy from a bag then picking another without replacing the first

Question 13

You roll three dice at the same time; one yellow, one red, and one purple. What is the probability of rolling a 6 on the yellow die, a 3 on the red die, and a 2 on the purple die?

Answer 13

• 1/216

Question 14

If a child has a 50% probability of being homozygous for a genetic condition, which of the following is a possible set of genotypes of the child’s parents?

Answer 14

• One parent is heterozygous for the condition; one parent is homozygous for the condition.

Question 15

When you cross an individual with the genotype AaBb with an individual with the genotype aaBB, what is the probability of producing offspring with the genotype aaBb?

Answer 15

• 1/4

Question 16

You toss a coin 4 consecutive times. Each time the result is heads. What is the probability of getting heads on your fifth toss of the coin?

Answer 16

• 50%

Question 17

If a woman is a carrier of a genetic disorder, what is the probability that one of her eggs will have the allele for the normal form of the trait?

Answer 17

• 50%