Given the parent genotype AaBbCCDDEe, what is the probability of each of these gametes forming?
a) ABCDE
b) either ABCDE or abCDE
Would the answer for a) be 1/8 and for b) be 1/2?
To calculate the probabilities of the gametes forming, let's break down the parent genotype AaBbCCDDEe into its individual alleles:
AaBbCCDDEe
From this genotype, we can identify 5 different alleles, represented as individual letters: A, B, C, D, and E.
Now let's consider the formation of the gametes:
a) ABCDE
In order for a gamete to have the ABCDE genotype, all five alleles (A, B, C, D, E) must be present. In the parent genotype AaBbCCDDEe, there are two possibilities for each allele: A or a, B or b, C or C, D or D, E or e.
Since the alleles segregate independently during gamete formation, the probability of each allele appearing in a gamete is 1/2. Therefore, to calculate the probability of the gamete having the genotype ABCDE, we multiply the probabilities of each allele appearing:
1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32.
So, the probability of the gamete ABCDE forming is 1/32.
b) either ABCDE or abCDE
To find the probability of either the ABCDE or abCDE gametes forming, we need to consider the probabilities of each individual gamete.
The probability of the ABCDE gamete forming is 1/32, as calculated above.
To calculate the probability of the abCDE gamete forming, we need to consider the probabilities of each allele in this specific genotype.
Since we want to find the probability of the lower case allele "a" appearing, we know that there is a 1/2 probability for each allele (A or a) to appear. Similarly, for each of the remaining alleles B, C, D, and E, there is a 1/2 probability.
So, the probability of the abCDE gamete forming is 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32.
Now, to find the probability of either the ABCDE or abCDE gametes forming, we simply add the probabilities of each individual gamete:
1/32 + 1/32 = 2/32 = 1/16.
Therefore, the probability of either the ABCDE or abCDE gametes forming is 1/16.