GeneticsStatistics and Probability

Chapter 3.8-3.9

Two major rules

1. Rule of multiplication (rule of and)

-The probability of two or more events occurring simultaneously is equal to the product of their individual probabilities.

Penny and Nickel

• Four possible outcomes:1. Penny, head: Nickel, head = (1/2) (1/2) = 1/4

2.Penny,tail: Nickel, head = (1/2) (1/2) = 1/4

3. Penny, head: Nickel, tail = (1/2) (1/2) = 1/4 4. Penny, tail : Nickel, tail = (1/2) (1/2) = 1/4

Application Part A: A couple learn that both are heterozygous

(carriers) for the same cystic fibrosis gene. What is the probability that their first child will have cystic fibrosis? What is the probability that their second child will have cystic fibrosis?

Part B: What is the probability that the couple's first

child will be a normal boy?

Rule of addition

2. Rule of addition ( rule of or) - The probability of obtaining any single

outcome, where that outcome can be achieved by two or more events, is equal to the sum of the individual probabilities of all such events.

Head or tail• What is the probability of tossing our penny and

nickel and obtaining one penny head and one nickel tail or tossing our penny and nickel and obtaining one penny tail and one nickel head?

- PennyHead:NickelTail = ¼ - PennyTail:NickelHead = ¼

(1/4) + (1/4) = 1/2

Chi-square

• Simplest statistical test for assessing the goodness of the null hypothesis.

• Null hypothesis assumes that there is no real difference between the measured values (or ratio) and the predicted values (or ratio).

-can either be rejected or fail to be rejected (random)

Formula

• O: observed values• E: expected values• Σ: sigma (sum of all classes considered)

Application

• What is the probability that a pea will be green or yellow if you cross Gg and Gg?

• Out of sample size of a thousand peas, the results observed were 740 of the peas were green and 260 were yellow. Use the chi-square formula to determine if the null hypothesis is rejected or fail to be rejected?

Remember…..

Interpret the chi-square number Degrees of freedom (df) is equal to n-1 (n is the

number of different categories into which the data is divided.

-n is the number of possible outcomes. n = 4; df = 3

Determining p

1. Locate the X2 value on the horizontal axis/x-axis.

2. Draw a vertical line from this point up to the line on the graph representing the appropriate df.

3. Extend a horizontal line to the left until it intersects the vertical axis/y-axis.

4. Estimate the corresponding p value.

Interpreting probability values• Think of p value as a percentage - 0.26 = 26% p value shows that a null hypothesis is never proved or

disproved. Standard: p value of 0.05 (chi-square 5%) * The null hypothesis is rejected when p ˂ 0.05