ANSC 221 (Exam3): G6-Probability

Definition of probability

Likelihood of an event occurring; calculated as Probability= # of times an event occurs/total number of events

Range of probability

Between 0 (never occurs) and 1 (always occurs)

All outcomes must sum to

1

Coin toss probability

Heads = ½, Tails = ½

Card deck probability

Ace of spades = 1/52, Not ace of spades = 51/52

Independent Events

One event does not affect the outcome of another

Genetic analogy for independent events

Allele segregation in gametes is like flipping coins

Multiplication Rule

Probability of two independent events occurring together = product of their probabilities

Example of Multiplication Rule

Prob(rr) = ½ (r from egg) × ½ (r from sperm) = ¼

Addition Rule

Probability of mutually exclusive events = sum of their probabilities

Example of Addition Rule

Prob(Rr or rR) = ¼ + ¼ = ½

Coat color in cattle

B = black (dominant), b = red (recessive)

Probability of red coat in cattle

Bb × Bb → Prob(red) = bb = ¼

Probability of black and male in cattle

Prob(black and male) = Prob(black) × Prob(male)

Dihybrid cross

YYRR and YyRR from YyRr × YyRr

Use of Punnett squares

Use Punnett squares and multiplication rule

Dog coat color genetics

B = black, b = red; D = pigment, d = diluted

Probability of black coat in dogs

BbDd × BbDd → Prob(black coat) = ?

Example cross for three characters

PpYyRr × Ppyyrr

Probability of recessive traits

Prob(≥2 recessive traits) = 6/16 = 37.5%

Large sample size effect

More accurate predictions

Real-world application of probability

Genetics, breeding, inheritance patterns

Coin toss combinations

Prob(HH), TT, HT, TH = each ¼

Tossing 2 coins 8 times

Explore outcomes

What is the probability of an event?

The chance that the event will occur in the future, calculated as the number of times an event occurs divided by the total number of events.

How do you calculate the probability of tossing heads with a coin?

The probability is ½.

What does a probability of 1 indicate?

An event that always occurs.

What does a probability of 0 indicate?

An event that never occurs.

What must the probabilities of all possible outcomes for an event add up to?

1.

What is the multiplication rule of probability?

The probability that two or more independent events will occur together is equal to the product of their respective probabilities.

How do you calculate the probability of a heterozygous F2 plant having wrinkled seeds (rr)?

Prob (rr) = Prob (r) x Prob (r) = ½ x ½ = ¼.

What is the addition rule of probability?

The probability that two or more mutually exclusive events will occur is equal to the sum of their individual probabilities.

How do you calculate the probability of an F2 plant being heterozygous (Rr)?

Prob (Rr) = ¼ + ¼ = ½.

What is the probability of two heterozygous parents (Bb x Bb) producing a black offspring?

Prob (BB or Bb) = ¼ + ½ = ¾.

What is the probability of two dihybrid parents (BbDd x BbDd) producing an offspring that is black?

Requires calculating the probabilities for black coat color based on the alleles.

What is the chance of finding offspring with at least two recessive traits from a cross of PpYyRr x Ppyyrr?

Prob (≥2 recessive) = 6/16 = 37.5%.

What happens to the accuracy of predictions as the sample size increases?

The results will conform more closely to the predictions.

How is segregation in a heterozygous individual similar to flipping a coin?

Each outcome is independent and unaffected by previous trials.

What is the probability of obtaining heads or tails when tossing two coins?

Each outcome has a probability of ¼.

What is the significance of the rules of probability in genetics?

They help predict the likelihood of various genetic outcomes.

What is the probability of producing an offspring that is black and male from two heterozygous parents?

Prob (black and male) = Prob (black) x Prob (male) = ¾ x ½ = 3/8.

What is the probability of producing the F2 genotypes YYRR and YyRR from dihybrid parents?

Requires calculating the probabilities for each genotype.

What does the term 'independent events' refer to in probability?

Events where the outcome of one event does not affect the outcome of another.

What is the formula for calculating simple probabilities?

Probability of an event = number of times an event occurs / total number of events.

What is the probability of picking a card other than the ace of spades from a standard deck?

51/52.

What does it mean if the probabilities of two events add up to more than 1?

It indicates an error in calculation, as probabilities must sum to 1.

What is the probability of a specific outcome in a genetic cross?

It can be calculated using the multiplication and addition rules of probability.

How can real-world scenarios apply the rules of probability?

They can be used to predict outcomes in various genetic crosses and breeding experiments.