Lesson 5 — Probability


Self-Check


By conducting the lab on coin tosses, you should have been able to make the connection between probabilities in genetics and everyday events. This takes some practice, but probabilities can help solve genetics problems faster than writing complete Punnett squares. To practise your skills, complete the following questions and check your answers. If you encounter any difficulty, consult with your teacher.


  1. The ability to taste the chemical PTC is determined by a single gene in humans. The ability to taste PTC is indicated by the dominant allele T and the inability to taste PTC by the recessive allele t. Suppose two heterozygous tasters (Tt) have a large family. 

    1. Predict the proportions of their children who will be tasters and non-tasters. Use a Punnett square to illustrate how you made this prediction.

    2. What is the likelihood that their first child will be a taster? What is the likelihood that their fourth child will be a taster?

    3. What is the likelihood that the first three children of this couple will be non-tasters?

  2. A husband and wife are both heterozygous for a recessive gene, c, for albinism. They were informed that the twins they are expecting are dizygotic, a boy and a girl.

    1. Draw a Punnett square of this cross.

    2. What are the chances that one child will be albino?

    3. What are the chances that both children will be normal?

    4. What are the chances that both babies will have the same phenotype for skin pigmentation?



Self-Check Answers


    1. Parental Cross: Tt x Tt
      Gametes: T and t

    2. T t
      T TT Tt
      t Tt tt

      «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mi»T«/mi»«mi»T«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mo»§#160;«/mo»«mi»T«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mi»t«/mi»«mi»a«/mi»«mi»s«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»s«/mi»«/math»

      «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mi»t«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mi»n«/mi»«mi»o«/mi»«mi»n«/mi»«mo»-«/mo»«mi»t«/mi»«mi»a«/mi»«mi»s«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»s«/mi»«/math»


    3. The probability that first child will be a taster is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«/math» or 0.75.
      The probability that fourth child will be a taster is also «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«/math» or 0.75. Each child is independent.
      These are not linked.

    4. Use the product rule for three independent events.
      The probability of having a non-taster is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«/math» for each child. The probability of having three non-tasters is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mi»x«/mi»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mn»64«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»016«/mn»«/math».


    1. C c
      C CC Cc
      c Cc cc

    2. The chance of having an albino child (cc) is 25%.   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»25«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»25«/mn»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mn»100«/mn»«mo»%«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»25«/mn»«mo»%«/mo»«/math»

    3. The chance of having a normal child is 75%. The probability of having two normal children is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»9«/mn»«mn»16«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»5625«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»5625«/mn»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mn»100«/mn»«mo»%«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»56«/mn»«mo».«/mo»«mn»25«/mn»«mo»%«/mo»«/math».

    4. The chance of having two albino children is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mn»16«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»0625«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»625«/mn»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mn»100«/mn»«mo»%«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»6«/mn»«mo».«/mo»«mn»25«/mn»«mo»%«/mo»«/math».

      The chance of having two normal children is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»9«/mn»«mn»16«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»5625«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»5625«/mn»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mn»100«/mn»«mo»%«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»56«/mn»«mo».«/mo»«mn»25«/mn»«mo»%«/mo»«/math».

      Then, the chance of having either two normal or two albino children is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»9«/mn»«mn»16«/mn»«/mfrac»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mn»16«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»10«/mn»«mn»16«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»5«/mn»«mn»8«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»625«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»625«/mn»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mn»100«/mn»«mo»%«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»62«/mn»«mo».«/mo»«mn»5«/mn»«mo»%«/mo»«mo»§#160;«/mo»«/math».

Diploma Connection


Answer the following questions from a previous Biology 30 Diploma Examination.



    Numerical Response

  1. In sheep, white wool is a dominant trait, and black wool is a recessive trait. In a herd of 500 sheep, 20 sheep have black wool. If two heterozygous sheep mated, what would be the probability of them having a white lamb?

    Answer: _____________



  2. Use the following information to answer the next question.

    Cystic fibrosis is the most common genetic disorder among Caucasians, affecting one in 2000 Caucasian children. The cystic fibrosis allele results in the production of sticky mucus in several structures, including the lungs and exocrine glands. Two parents who are unaffected by the disorder can have a child with the disorder.


    Numerical Response

  3. A pair of parents who are unaffected by cystic fibrosis are planning to have another child. What is the chance that their next child will be affected by cystic fibrosis? (Record your answer as a whole number.)

    Answer:          _____________ %



  4. Use the following information to answer the next question.

    Marfan syndrome is an autosomal dominant disorder of humans. Affected individuals tend to be tall and thin. They have defects in the lens of the eye and weak connective tissue around the aorta. Often, affected individuals excel in sports such as volleyball or basketball, but it is not uncommon for people with this syndrome to die suddenly.


    Numerical Response

  5. A man heterozygous for Marfan syndrome and a homozygous recessive woman have a child. What is the probability that the child will be affected by Marfan syndrome? (Record your answer as a value from 0 to 1, rounded to two decimal places.)

    Answer:          _____________



  6. Use the following information to answer the next question.

    Scientists believe that a mutant form of an autosomal gene called BRCA1 may be associated with 5% to 10% of all cases of breast cancer. About 80% of women who inherit the gene in its defective form are likely to develop cancerous breast tumors. Men who carry the faulty BRCA1 gene rarely develop breast cancer, but they may pass the gene to their offspring.

    A couple has two children, a girl and a boy. The mother has a single mutant gene for breast cancer; the father is not a carrier of the mutant BRCA1 gene.

  7. What is the chance that their daughter has inherited the mutant BRCA1 gene?
    1. 75%
    2. 50%
    3. 25%
    4. 0%

Diploma Question Answers


  1. 0.75

    W w
    W WW Ww
    w Ww ww

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«/math» = 0.75 of their offspring will have white wool.

  2. This is an autosomal recessive situation. If neither or one parent has the allele, there is no way the child can have the condition, 0%. If both parents carry the allele, then there is 25% that the child will have the condition. Let F be the dominant unaffected allele, and f be the recessive, cystic fibrosis allele.

    Neither of the parents have the allele

     F  F
     F  FF  FF
     F  FF  FF

    None of their children will be affected.
    One parent has the allele

     F  f
     F  FF  Ff
     F  FF  Ff

    There is 50% chance that their children will carry the allele but none of their children will be affected.
     Both parents carry the allele

     F  f
     F  FF  Ff
     f  Ff  ff

    There is 25% chance that their children will be affected by cystic fibrosis.


  3. This is an autosomal dominant situation. Half the children will have the allele: 0.50.

     M  m
     m  Mm  mm
     m  Mm  mm


  4. 50% of the daughters will have the mutant gene. This mutant gene is not related to the sex of the offspring. Therefore, 50% of the daughters and 50% sons will have the mutant gene.

     B  B
     B  BB  BB
     b  Bb  Bb


Biology 30 © 2008  Alberta Education & its Collaborative Partners ~ Updated by ADLC 2019