Probability and Genetics

PROBABILITY AND GENETICS

Probability: is the chance or likelihood of a particular outcome (event) expressed as a ratio.

A probability will have a range between 0 -1.

The sum of the probabilities must add up to 1.

Example:

Using a two headed coin, a) what is the probability of tossing heads? 1

b) what is the probability of tossing tails? 0

c) what is the sum of the probabilities? 1 + 0 = 1

Using a two headed coin a) what is the probability of tossing heads? 1/2

b) what is the probability of tossing tails? 1/2

c) what is the sum of the probabilities? 1/2 + 1/2 = 1

Using a deck of cards a) what is the probability of drawing the queen of hearts? 1/52

b) what is the probability of drawing any other card? 51/52

c) what is the sum of the probabilities? 1

Using a die a) what is the probability of rolling a 3? 1/6

b) what is the probability of rolling a 6? 1/6

c) what is the probability of rolling any other number? 4/6

d) what is the sum of the probabilities? 1

In tossing a coin, what ever happened during the first toss is independent of the outcome of the second toss.

Therefore successive coin tosses are independent events.

In a series of five tosses, five heads were obtained. What is the possibility that the sixth toss will be heads? be tails?

When working with probabilities there are two basic laws of probability that can be used when solving genetic problems;

a) RULE OF MULTIPLICATION and

b) RULE OF ADDITION. RULE OF MULTIPLICATION

Take two coins are toss at the same time. Remember that each toss is independent of the other.

What is the probability that both coins will turn up heads? ______

In order to determine this probability you must

i) calculate the probability of each independent event

ii) multiply each individual probability to obtain an overall probability of these events occurring in combination.

Fraction Percent

What is the probability that the first coin will be heads? 1/2 50%

What is the probability that the second coin will be heads? 1/2 50 %

What is the probability that BOTH coins will be heads? 1/2 x 1/2 = 1/4 25%

The concept of a coin toss is similar to the events that would take place in a monohybrid cross.

Example: In flower colour a red (R) flower is dominant to a white (r) flower. If both parents are heterozygous red (Rr), What is the probability that they would produce a white flower?

Remember the law of segregation states that like alleles must segregate (separate) from each other.

Phenotype Red Red

Genotype Rr Rr

segregation segregation of alleles of alleles

Gamete 1/2 R 1/2 r 1/2 R 1/2 r

What is the probability of two recessive (r) alleles coming together at fertilization? (Hint probability of two heads)

Each event is independent of each other. In the male plant half (1/2) the gametes will contain the recessive allele r. The same is true for the female plant in that half (1/2) the gametes will contain the recessive allele r. The probability that both of these alleles will come together is the product of each independent event.

1/2 x 1/2 = 1/4 (similar to tossing two coins and both coins turning up heads)

There is a 25% chance that a white flowered offspring will be produced. THE RULE OF ADDITION

Rule of Addition: the probability of an event that can occur in two or more different ways is the sum of the separate probabilities of those ways.

Example: Assume both plants are heterozygous red (Rr). What is the probability that they would produce an offspring that is heterozygous red (Rr)?

Phenotype Red Red Genotype Rr Rr

Gamete 1/2 R 1/2 r 1/2 R 1/2 r

There are two possible events that could take place.

a) the dominant allele comes from the egg and the recessive allele comes from the pollen.

Probability = 1/2 R (egg) x 1/2 r (pollen) = 1/4 Rr

b) the dominant allele comes from the pollen and the recessive allele comes from the egg.

Probability = 1/2 R (pollen) x 1/2 r (egg) = 1/4 Rr

Because these are two possible events that could take place, the probability is the sum of the two separate events

1/4 + 1/4 = 2/4

There is a 50% chance that a heterozygous red plant would be produced.

These probabilities can be easily calculated by using a punnet square.

Example: Two heterozygous red plants are cross-pollinated, determine the probability of producing red and white offspring's.

Egg 1/2 R 1/2 r Probability of each Pollen independent event

1/2 R 1/4 RR 1/4 Rr

Probability of each Probability of these event independent event occurring in combination. 1/2 r 1/4 Rr 1/4 rr

Probability of having a Genotype Probability Fraction Percentage Ratio

homozygous red is RR 1/2 R x 1/2 R 1/4 25% 1 heterozygous red is Rr 1/2R x 1/2r 1/4 1/4 + 1/4 =1/2 50% 2 heterozygous red is Rr 1/2r x 1/2R 1/4 homozygous white is rr 1/2 r x 1/2 r 1/4 25% 1 PROBABILITY AND GENETICS

Probability: ______

A probability will have a ______.

The ______of the probabilities must ______.

Example:

Using a two headed coin, a) what is the probability of tossing heads? ______

b) what is the probability of tossing tails? ______

c) what is the sum of the probabilities? ______

Using a two headed coin a) what is the probability of tossing heads? ______

b) what is the probability of tossing tails? ______

Using a deck of cards a) what is the probability of drawing the queen of hearts? ______

b) what is the probability of drawing any other card? ______

Using a die a) what is the probability of rolling a 3? ______

b) what is the probability of rolling a 6? ______

c) what is the probability of rolling any other number? ______

d) what is the sum of the probabilities? ______

In tossing a coin, what ever happened during the first toss is ______of the outcome of the second toss.

Therefore successive coin tosses are independent events.

In a series of five tosses, five heads were obtained. What is the possibility that the sixth toss will be heads? be tails?

When working with probabilities there are two basic laws of probability that can be used when solving genetic problems;

a) ______and

b) ______RULE OF MULTIPLICATION

Take two coins are toss at the same time. Remember that each toss is independent of the other.

What is the probability that both coins will turn up heads? ______

In order to determine this probability you must

i) ______

ii) ______

______

Fraction Percent

What is the probability that the first coin will be heads?

What is the probability that the second coin will be heads?

What is the probability that BOTH coins will be heads?

The concept of a coin toss is similar to the events that would take place in a ______.

Example: In flower colour a red (R) flower is dominant to a white (r) flower. If both parents are heterozygous red (Rr), What is the probability that they would produce a white flower?

Remember the law of segregation states that like alleles must segregate (separate) from each other.

Phenotype

Genotype

Gamete

What is the probability of two recessive (r) alleles coming together at fertilization? (Hint probability of two heads)

Each event is independent of each other. In the ______the gametes will contain the recessive allele r. The same is true for the ______the gametes will contain the recessive allele r. The probability that both of these alleles will come together is the ______. THE RULE OF ADDITION

Rule of Addition: the probability of an event that can occur in ______is the ______of the ______of those ways.

Example: Assume both plants are heterozygous red (Rr). What is the probability that they would produce an offspring that is heterozygous red (Rr)?

Phenotype Red Red Genotype Rr Rr

Gamete 1/2 R 1/2 r 1/2 R 1/2 r

There are two possible events that could take place.

a) the dominant allele comes from the egg and the recessive allele comes from the pollen.

b) the dominant allele comes from the pollen and the recessive allele comes from the egg.

Because these are two possible events that could take place, the probability is the sum of the two separate events

These probabilities can be easily calculated by using a ______-.

Example: Two heterozygous red plants are cross-pollinated, determine the probability of producing red and white offspring's.

Egg 1/2 R 1/2 r Probability of each Pollen independent event

Probability of each independent event 1/2 r

Probability of having a Genotype Probability Fraction Percentage Ratio

homozygous red is

heterozygous red is

homozygous white is