Use Probability for Inheritance Predictions - Biology

1. What is $P(\text{both children are } aa)$ if each child has $P(aa)=\frac{1}{4}$ and births are independent?

   $\frac{1}{16}$. Independent events multiply: $\frac{1}{4} \times \frac{1}{4}$.

2. What is the probability rule that justifies multiplying probabilities across different genes in a dihybrid cross?

   Independent assortment (treat events as independent). Genes on different chromosomes assort independently during meiosis.

3. What is $P(AAbb)$ in the cross $AaBb \times AaBb$ (independent assortment)?

   $\frac{1}{16}$. Homozygous dominant A, homozygous recessive b.

4. What is the genotype ratio from a monohybrid cross $Aa \times Aa$?

   $1AA:2Aa:1aa$. Classic Mendelian ratio from heterozygous parents.

5. What is $P(\text{at least one recessive phenotype})$ in $Aa \times Aa$?

   $\frac{1}{4}$. Recessive phenotype probability in monohybrid cross.

6. What is $P(\text{intermediate phenotype})$ for incomplete dominance in $Rr \times Rr$?

   $\frac{1}{2}$. Heterozygotes ($Rr$) show the intermediate pink phenotype.

7. What is $P(Aa)$ for the cross $Aa \times Aa$?

   $\frac{1}{2}$. Heterozygous offspring from two heterozygous parents.

8. What is $P(A_{bb})$ in the cross $AaBb \times AaBb$ with independent assortment?

   $\frac{3}{16}$. Dominant for A, recessive for B in dihybrid cross.

9. What is the phenotype ratio for incomplete dominance in the cross $Rr \times Rr$?

   $1$ red : $2$ pink : $1$ white. Heterozygotes show a blended intermediate phenotype.

10. What is $P(\text{recessive phenotype})$ in the test cross $Aa \times aa$?

    $\frac{1}{2}$. Half the offspring are recessive in test cross.

11. What is the complement rule for a genetic outcome that does not occur?

    $P(\text{not }A)=1-P(A)$. The probability of not getting an outcome equals 1 minus its probability.

12. What is $P(\text{dominant phenotype})$ for $Aa \times Aa$ with complete dominance?

    $\frac{3}{4}$. Both $AA$ and $Aa$ show dominant phenotype.

13. What is the addition rule for mutually exclusive genetic outcomes?

    $P(A \text{ or } B)=P(A)+P(B)$. Mutually exclusive outcomes add their probabilities.

14. What is $P(aa)$ for the cross $Aa \times Aa$ with complete dominance?

    $\frac{1}{4}$. Only $aa$ shows recessive phenotype in complete dominance.

15. What does the probability of an event represent in genetics problems?

    The likelihood that a specific genotype or phenotype occurs. Probability quantifies the chance a genetic outcome will occur.

16. What is $P(\text{roan})$ for codominance in $C^RC^W \times C^RC^W$?

    $\frac{1}{2}$. Heterozygotes express both red and white alleles simultaneously.

17. What is the genotype ratio for the ABO cross $I^Ai \times I^Bi$?

    $\frac{1}{4}$ each: $I^AI^B$, $I^Ai$, $I^Bi$, $ii$. Each genotype appears in $\frac{1}{4}$ of offspring.

18. What is $P(aabb)$ in the cross $AaBb \times AaBb$ with independent assortment?

    $\frac{1}{16}$. Recessive phenotype for both traits in dihybrid cross.

19. What is $P(\text{not recessive phenotype})$ in $Aa \times Aa$ with complete dominance?

    $\frac{3}{4}$. Complement of recessive phenotype probability.

20. What is $P(\text{dominant for both})$ using the product rule if $P(A_)=\frac{3}{4}$ and $P(B_)=\frac{3}{4}$?

    $\frac{9}{16}$. Multiply independent probabilities: $\frac{3}{4} \times \frac{3}{4}$.

21. What is the expected phenotype ratio in a test cross $Aa \times aa$ (complete dominance)?

    $1$ dominant : $1$ recessive. Equal probability of dominant and recessive phenotypes.

22. What is the probability an offspring receives allele $A$ from a heterozygous parent $Aa$?

    $\frac{1}{2}$. Equal probability of transmitting either allele.

23. What is $P(\text{type AB})$ for the ABO cross $I^Ai \times I^Bi$?

    $\frac{1}{4}$. Only $I^AI^B$ genotype produces type AB blood.

24. What is $P(\text{offspring has genotype } Aabb)$ in $AaBb \times AaBb$ (independent assortment)?

    $\frac{1}{8}$. Heterozygous A, homozygous recessive b.

25. What is $P(\text{all 3 children show dominant phenotype})$ if each has probability $\frac{3}{4}$?

    $\left(\frac{3}{4}\right)^3=\frac{27}{64}$. Independent events multiply: $\left(\frac{3}{4}\right)^3$.

26. What is $P(\text{dominant for both})$ using the product rule if $P(A\_)=\frac{3}{4}$ and $P(B\_)=\frac{3}{4}$?

    $\frac{9}{16}$. Multiply independent probabilities: $\frac{3}{4} \times \frac{3}{4}$.

27. What is $P(aaB\_)$ in the cross $AaBb \times AaBb$ with independent assortment?

    $\frac{3}{16}$. Recessive for A, dominant for B in dihybrid cross.

28. What does "homozygous recessive" mean for a single gene with two alleles?

    Two recessive alleles (for example, $aa$). Two copies of the recessive allele at the same locus.

29. What is $P(\text{recessive phenotype})$ for the cross $AA \times Aa$?

    $0$. Homozygous dominant parent cannot produce recessive offspring.

30. What is $P(\text{offspring is heterozygous at both loci } AaBb)$ in $AaBb \times AaBb$?

    $\frac{1}{4}$. Heterozygous at both loci in dihybrid cross.

31. What is the phenotype ratio for codominance in the cross $C^RC^W \times C^RC^W$?

    $1$ red : $2$ roan : $1$ white. Both alleles are expressed simultaneously in heterozygotes.

32. What is $P(\text{at least one } aa)$ in two children if each has $P(aa)=\frac{1}{4}$?

    $1-\left(\frac{3}{4}\right)^2=\frac{7}{16}$. Use complement rule: 1 minus probability of no $aa$ children.

33. What is the probability of producing gamete $AB$ from genotype $AaBb$ (independent assortment)?

    $\frac{1}{4}$. Each of four possible gamete types equally likely.

34. What is $P(\text{type O})$ for the ABO cross $I^Ai \times I^Bi$?

    $\frac{1}{4}$. Only $ii$ genotype produces type O blood.

35. What is $P(A\_B\_)$ in the cross $AaBb \times AaBb$ with independent assortment?

    $\frac{9}{16}$. Dominant phenotype for both traits using independent assortment.

36. What is the multiplication rule for independent genetic events?

    $P(A \text{ and } B)=P(A)\times P(B)$. Independent events multiply their individual probabilities.

37. What does "heterozygous" mean for a single gene with two alleles?

    Two different alleles (for example, $Aa$). One dominant and one recessive allele at the same locus.

38. What is $P(\text{dominant phenotype})$ in the test cross $Aa \times aa$?

    $\frac{1}{2}$. Half the offspring show each phenotype in test cross.

39. What is the classic dihybrid phenotype ratio from $AaBb \times AaBb$ (independent assortment)?

    $9:3:3:1$. Standard ratio for two independent genes with complete dominance.

40. What is a test cross used to determine in inheritance probability problems?

    Whether a dominant-phenotype individual is heterozygous or homozygous. Reveals hidden genotype by crossing with homozygous recessive.

41. What is the probability an offspring receives allele $a$ from a homozygous recessive parent $aa$?

    $1$. Homozygous parent only has one allele type.

42. What is the phenotype ratio with complete dominance from $Aa \times Aa$?

    $3$ dominant : $1$ recessive. Dominant allele masks recessive in heterozygotes.

43. What is $P(\text{exactly one } aa)$ in two children if each has $P(aa)=\frac{1}{4}$?

    $2\times\frac{1}{4}\times\frac{3}{4}=\frac{3}{8}$. Binomial probability: one success, one failure, times 2 orders.

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