What is the probability that each of the following pairs of parents will produce

Question

What is the probability that each of the following pairs of parents will produce the indicated offspring? (Assume independent assortment of all gene pairs.) AABBCC times aabbcc rightarrow AaBbCc AABbCc times AaBbCc rightarrow AAbbCC AaBbCc times AaBbCc rightarrow AaBbCc aaBbCC times AABbcc rightarrow AaBbCc Karen and Steve each have a sibling with sickle-cell disease. Neither Karen Steve nor of their parents have the disease, and none of them have been tested to see if they have the sickle-cell trait. Based on this incomplete calculate the probability that if this couple has a child, the child will have sickle-cell disease. In 1981, a stray black cat with unusual rounded, curled-back ears was adopted by a family in California. Hundreds of descendants of the cat have since been born, and cat fanciers hope to develop the curl cat into a show breed. Suppose you owned the first curl cat and wanted to develop a true-breeding variety. How would you determine whether the curl allele is dominant or recessive? How would you obtain true-breeding curl cats? How could you be sure they are true-breeding?

Explanation / Answer

8. (i) AABBCC x aabbcc = AaBbCc

There is only one combination possible between AA and aa that is Aa, so it is 1.

There is only one combination possible between BB and bb that is Bb, so it is 1.

There is only one combination possible between CC and cc that is Cc, so it is 1.

The probability for AaBbCc is 1x1x1 = 1 (100% chances to get this offspring)

(ii) AABbCc x AaBbCc = AAbbCC

There are two combination possible between AA and Aa that is Aa and AA, so it is 1/2.

There are four combination possible between Bb and Bb that is Bb, BB, bb and bB, so it is 1/4

There are four combination possible between Cc and Cc that is Cc, CC, cC and cc, so it is 1/4

The probability for AAbbCC is 1/2x1/4x1/4 = 1/32 (3.125% chance to get this offspring)

(iii) AaBbCc x AaBbCc = AaBbCc

Four combinations between Aa and Aa that is AA, Aa, aA and aa, so it is 2/4 = 1/2

Four combinations between Bb and Bb that is BB, Bb, bB and bb, so it is 2/4 = 1/2

Four combinations between Cc and Cc that is CC, Cc, cC and cc, so it is 2/4 = 1/2

The probability for AaBbCc is 1/2x1/2x1/2 = 1/8 (12.5% chance of getting this offspring)

(iv) aaBbCC x AABbcc = AaBbCc

One combination between aa and AA that is Aa, so it is 1

Four combinations between Bb and Bb that is BB, Bb, bB and bb, so it is 2/4 = 1/2

One combination possible between CC and cc that is Cc, so it is 1.

The probability for AaBbCc is 1x1/2x1 = 1/2 (50% chance to get this offspring)

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