Chapter 2. Chapter 2: Using Punnett Squares and Probability to Analyze a Pedigree

Introduction

Unpacking the Problem
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You must read each slide, and complete any questions on the slide, in sequence.

A man's paternal grandfather had galactosemia. This is a rare disease caused by the inability to process galactose, leading to muscle, nerve, and kidney malfunction. The man married a woman whose sister had galactosemia but whose parents did not. The woman is now pregnant with their first child.

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (step 1): Draw the pedigree as described.
  • Part B (steps 2-9): Decide what the probability is that this child will have galactosemia.
  • Part C (step 10): Resolve what the probability is that a second child will have galactosemia if the first child does, in fact, have it.

Question

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1

A man's paternal grandfather had galactosemia. This is a rare disease caused by the inability to process galactose, leading to muscle, nerve, and kidney malfunction. The man married a woman whose sister had galactosemia but whose parents did not. The woman is now pregnant with their first child.

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (step 1): Draw the pedigree as described.
  • Part B (steps 2-9): Decide what the probability is that this child will have galactosemia.
  • Part C (step 10): Resolve what the probability is that a second child will have galactosemia if the first child does, in fact, have it.

Question

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1

A man's paternal grandfather had galactosemia. This is a rare disease caused by the inability to process galactose, leading to muscle, nerve, and kidney malfunction. The man married a woman whose sister had galactosemia but whose parents did not. The woman is now pregnant with their first child.

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (step 1): Draw the pedigree as described.
  • Part B (steps 2-9): Decide what the probability is that this child will have galactosemia.
  • Part C (step 10): Resolve what the probability is that a second child will have galactosemia if the first child does, in fact, have it.

Question

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
1

A man's paternal grandfather had galactosemia. This is a rare disease caused by the inability to process galactose, leading to muscle, nerve, and kidney malfunction. The man married a woman whose sister had galactosemia but whose parents did not. The woman is now pregnant with their first child.

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (step 1): Draw the pedigree as described.
  • Part B (steps 2-9): Decide what the probability is that this child will have galactosemia.
  • Part C (step 10): Resolve what the probability is that a second child will have galactosemia if the first child does, in fact, have it.

Question

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
1

A man's paternal grandfather had galactosemia. This is a rare disease caused by the inability to process galactose, leading to muscle, nerve, and kidney malfunction. The man married a woman whose sister had galactosemia but whose parents did not. The woman is now pregnant with their first child.

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (step 1): Draw the pedigree as described.
  • Part B (steps 2-9): Decide what the probability is that this child will have galactosemia.
  • Part C (step 10): Resolve what the probability is that a second child will have galactosemia if the first child does, in fact, have it.

Question

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1

A man's paternal grandfather had galactosemia. This is a rare disease caused by the inability to process galactose, leading to muscle, nerve, and kidney malfunction. The man married a woman whose sister had galactosemia but whose parents did not. The woman is now pregnant with their first child.

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (step 1): Draw the pedigree as described.
  • Part B (steps 2-9): Decide what the probability is that this child will have galactosemia.
  • Part C (step 10): Resolve what the probability is that a second child will have galactosemia if the first child does, in fact, have it.

Question

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
1

A man's paternal grandfather had galactosemia. This is a rare disease caused by the inability to process galactose, leading to muscle, nerve, and kidney malfunction. The man married a woman whose sister had galactosemia but whose parents did not. The woman is now pregnant with their first child.

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (step 1): Draw the pedigree as described.
  • Part B (steps 2-9): Decide what the probability is that this child will have galactosemia.
  • Part C (step 10): Resolve what the probability is that a second child will have galactosemia if the first child does, in fact, have it.

Question

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1

A man's paternal grandfather had galactosemia. This is a rare disease caused by the inability to process galactose, leading to muscle, nerve, and kidney malfunction. The man married a woman whose sister had galactosemia but whose parents did not. The woman is now pregnant with their first child.

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (step 1): Draw the pedigree as described.
  • Part B (steps 2-9): Decide what the probability is that this child will have galactosemia.
  • Part C (step 10): Resolve what the probability is that a second child will have galactosemia if the first child does, in fact, have it.

Question

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1

A man's paternal grandfather had galactosemia. This is a rare disease caused by the inability to process galactose, leading to muscle, nerve, and kidney malfunction. The man married a woman whose sister had galactosemia but whose parents did not. The woman is now pregnant with their first child.

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (step 1): Draw the pedigree as described.
  • Part B (steps 2-9): Decide what the probability is that this child will have galactosemia.
  • Part C (step 10): Resolve what the probability is that a second child will have galactosemia if the first child does, in fact, have it.

Question

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1

A man's paternal grandfather had galactosemia. This is a rare disease caused by the inability to process galactose, leading to muscle, nerve, and kidney malfunction. The man married a woman whose sister had galactosemia but whose parents did not. The woman is now pregnant with their first child.

Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.

  • Part A (step 1): Draw the pedigree as described.
  • Part B (steps 2-9): Decide what the probability is that this child will have galactosemia.
  • Part C (step 10): Resolve what the probability is that a second child will have galactosemia if the first child does, in fact, have it.

Question

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1

General Hints

When analyzing a pedigree, there are a few rules of thumb:

  • If two affected parents have an unaffected kid, it is NOT recessive.
  • If unaffected parents have an affected kid, it is NOT dominant.
  • If unaffected parents have an affected daughter, it is NOT dominant or x-linked recessive.
  • If an unaffected woman has an affected son, it is NOT x-linked dominant.
  • If an affected man has an unaffected daughter, it is NOT x-linked dominant.
  • If an affected woman has an unaffected son, it is NOT x-linked recessive.
  • If an unaffected man has an affected daughter, it is NOT x-linked recessive.

When calculating probabilities, two rules are useful for predicting the ratios of offspring produced in genetic crosses:

  • Multiplication Rule: the probability of two or more independent events occurring together is calculated by multiplying their independent probabilities. e.g., the probability of rolling a die twice and obtaining two threes.
  • Addition Rule: the probability of any one of two or more mutually exclusive events is calculated by adding the probabilities of these events. e.g., the probability of rolling either a two or a three.

Punnett squares are also useful tools for determining probability. If you see a certain ratio of affected to unaffected individuals in a generation, it may be helpful to draw the Punnett square to determine the genotype of the parent. For instance, if both the parents are carriers of a recessive trait, you would expect to see a 3:1 ratio, whereas if only one parent is a carrier, you would not have any affected offspring. If an heterozygote is crossed to a homozygous individual (a testcross), you would expect a 1:1 ratio in the progeny. Similarly, a cross between two heterozygotes would yield a 3:1 ratio if it is an example of dominance, or a 1:2:1 ratio if it is "incomplete dominance." This can be easily visualized by drawing Punnett squares with each of the possible genotypes represented.

To Summarize

So, there are a couple of rules to remember when analyzing a pedigree and calculating probability.

In general, if a trait is expressed in every generation, it is probably dominant. If it skips generations, it is probably recessive. Finally, if it seems to affect males more often than females, it is likely to be x-linked.

The probability of having a particular genotype can be calculated using either the product or addition rules. If you want to examine the probability of two children inheriting a particular trait, you would use the multiplication rule. The probabilities are multiplied together to determine the probability of two or more independent events occurring together. If you want to examine the probability of at least one of the two children inheriting a particular trait, you would use the addition rule. The probability of any one of two or more mutually exclusive events is calculated by adding the probabilities of these events.