BIO207H5S Dihybrid and Trihybrid Crosses with Probability Rules

Dihybrid Cross

• In a dihybrid cross, the probability of obtaining offspring with the genotype RRYYCC from the selfing of the F1 generation is unknown in this context.

Probability of Genotype

• The probability of an offspring from the cross Aa Bb Cc dd Ee having the genotype Aa Bb Cc dd Ee is unknown in this context.

Chi-Square (𝛘2) Goodness-of-Fit Test

• The Chi-Square (𝛘2) Goodness-of-Fit Test indicates whether the observed frequencies differ significantly from the expected frequencies in genetics.
• The null hypothesis in the context of the Chi-Square (𝛘2) Goodness-of-Fit Test is that the observed frequencies do not differ significantly from the expected frequencies.
• The degrees of freedom (d.o.f) in the context of the Chi-Square (𝛘2) Goodness-of-Fit Test depend on the number of classes minus one.

Forked Line/Branch Diagram

• The Forked line/Branch Diagram helps to illustrate the possible genotypes and phenotypes of offspring from a cross between two parents with different genotypes.

Chi-Square Test

• If the calculated 𝛘2 value is less than the critical value, it indicates that the observed frequencies do not differ significantly from the expected frequencies.
• If the calculated 𝛘2 value is greater than or equal to the critical value, it indicates that the observed frequencies differ significantly from the expected frequencies.

Probability of Events

• The probability of having at least four girls in a family of six children, if the probability of having a girl is 1/2, can be calculated using the binomial expansion.

Critical Value

• The critical value P(0.01) at 2 degrees of freedom in a chi-square test signifies the probability of observing a result as extreme or more extreme than the one observed, assuming that the null hypothesis is true.
• The critical value P(0.10) at 4 degrees of freedom in a chi-square test signifies the probability of observing a result as extreme or more extreme than the one observed, assuming that the null hypothesis is true.

Binomial Expansion

• The binomial expansion helps calculate the probability of a certain number of events occurring in a fixed number of trials, given the probability of the event occurring in a single trial.
• In the binomial expression n = 8, x = 3, and p = 0.4, q represents the probability of the event not occurring in a single trial (q = 1 - p = 0.6).

Monohybrid Cross

• The problem-solving approach that involves using the chi-square test for a monohybrid cross is unknown in this context.

Interpretation of Chi-Square Test

• A calculated 𝛘2 value less than the critical value indicates that the observed frequencies do not differ significantly from the expected frequencies.
• Scientists typically assume that the null hypothesis is rejected when P < 0.05 in a chi-square test, indicating that the observed frequencies differ significantly from the expected frequencies.