probability & punnett squares

Probability & Punnett Squares

Probability • A concept that can be

used to predict the results of a particular event– Examples

• Chance of a specific team winning a sporting event

• Chance of a coin landing on heads in a coin toss

– Predict what is likely to occur, not necessarily what will actually occur

Probability and Heredity• Think back to Mendel’s

plant experiments– He noticed that traits were

inherited in patterns• For example, when he

crossed two plants that were heterozygous for stem height (Tt) he noticed their offspring would inherit this trait in a predictable pattern, with 3 out of 4 having tall stem height.

Probability and Heredity• Each time Mendel

repeated the cross, he would obtain similar results

• He could say that the probability, or chance, of the cross producing a tall plant was 3 in 4 and the probability of producing a short plant was 1 in 4.

Mendel noticed the same pattern of inheritance in other traits as well

Probability and Punnett Squares

• Punnett Square – A chart that shows how parents’ alleles might combine in an offspring– a tool that can help you understand the patterns of

heredity– Geneticists use Punnett Squares to show all the

possible outcomes of a genetic cross and to determine the probability of a particular outcome

– Punnett Squares Explained at http://www.siskiyous.edu/class/bio1/genetics/monohybrid_v2.html

Probability and Punnett Squares

• What is the probabilty of…..– The offspring having a

yellow seed color?2 in 4 – The offspring having a

green seed color? 2 in 4

Probability and Punnett Squares

• How else can probability be written?

– The offspring having a yellow seed color?

2 in 4 or 50% – The offspring having a

green seed color? 2 in 4 or 50%

Using a Punnett Square

• In rabbits, black fur color is dominant to white. What is the probability of producing a white rabbit if two heterozygous rabbits mate?

Using a Punnett Square• Step 1: figure out the

genotype of the parents.

• Black is dominant to white. – B - black– b - white

• Parents are heterozygous.– Bb - dad– Bb - mom

Using a Punnett Square

• Step 2: set up a Punnett Square.

B b

B

b

BbBb

Using a Punnett Square

• Step 3: Fill in the Punnett Square.

B b

B

b

Using a Punnett Square

• Step 3: Fill in the Punnett Square.

B b

B

b

BB

Using a Punnett Square

• Step 3: Fill in the Punnett Square.

B b

B

b

BB Bb

Using a Punnett Square

• Step 3: Fill in the Punnett Square.

B b

B

b

BB Bb

Bb

Using a Punnett Square

• Step 3: Fill in the Punnett Square.

B b

B

b

BB Bb

Bb bb

Using a Punnett Square

• Step 4: Count the results.

• Genotypes – 1 homozygous

dominant

B b

B

b

BB Bb

Bb bb

Using a Punnett Square

• Step 4: Count the results.

• Genotypes – 1 homozygous

dominant– 2 heterozygotesB b

B

b

BB Bb

Bb bb

Using Punnett Square

• Step 4: Count the results.

• Genotypes – 1 homozygous

dominant– 2 heterozygotes– 1 homozygous

recessive

B b

B

b

BB Bb

Bb bb

Using a Punnett Square

• Step 4: Count the results.

• Genotypes – 1 homozygous

dominant– 2 heterozygotes– 1 homozygous

recessive• Phenotypes

B b

B

b

BB Bb

Bb bb

Using a Punnett Square

• Step 4: Count the results.

• Genotypes – 1 homozygous

dominant– 2 heterozygotes– 1 homozygous

recessive• Phenotypes

– 3 black fur

B b

B

b

BB Bb

Bb bb

Using a Punnett Square

• Step 4: Count the results.

• Genotypes – 1 homozygous

dominant– 2 heterozygotes– 1 homozygous

recessive• Phenotypes

– 3 black fur– 1 white fur

B b

B

b

BB Bb

Bb bb

Probability and Punnett Squares

• In rabbits, black fur color is dominant to white. What is the probability of producing a white rabbit if two heterozygous rabbits mate? – 1 in 4 or 25%

Representing Ratios

• Probability can also be represented in ratios– A ratio compares or shows the relationship

between a part to the whole• Example the probability that a coin will land on

heads in a single coin toss is 1 in 2 or 50%– As a ratio, the probability would be written as

1:2 and would be read as, “One to two.”– In genetics we use rations to represent

probability

Using a Punnett Square• Step 4: Count the

results. • Genotypes =

– 1 homozygous dominant

– 2 heterozygotes– 1 homozygous

recessive– Genotypic Ratio =

1:2:1• Phenotypes

– 3 black fur– 1 white fur

B b

B

b

BB Bb

Bb bb

Using a Punnett Square• Step 4: Count the results. • Genotypes =

– 1 homozygous dominant– 2 heterozygotes– 1 homozygous recessive– Genotypic Ratio = 1:2:1

• Phenotypes– 3 black fur– 1 white fur– Phenotypic Ratio = 3:1

B b

B

b

BB Bb

Bb bb

Let’s Practice1. In pine trees, long

needles are dominant over short needles. Cross a homozygous dominant plant with a plant that is heterozygous. What is the probability that the parents will produce offspring that have short needles? Give the genotypic and phenotypic ratios.

Let’s Practice 2. In cats, a striped coat is dominant over a solid coat. Cross a cat with a solid coat with a cat that is heterozygous for a striped coat. What is the probability that the parents will produce offspring with a solid coat? Give the genotypic and phenotypic ratios.

Let’s Practice 3. In humans, dark hair is dominant over light hair. Cross a man that is homozygous recessive with a woman that is homozygous dominant. What is the probability that the parents will produce offspring with light hair? Give the genotypic and phenotypic ratios.