Homework Answers
The binomial theorem is used when the total outcome or the total number of offsprings are mentioned in the question.
The binomial theorem equation formula is:-
n! / s! t! x (a)s (b)t
Where, a = probability of outcome 1 (for example - will have the disease)
b = probability of outcome 2 (for example - will not have the disease)
So, according to the question,
n (total no. of progeny / offspring) = 7
s (diseased) = 3
t (normal) = 4
And as both, the parents are heterozygous for the disease sickle cell anemia,
Therefore;
Mother (Aa) x Father (Aa)
F1 = Aa
F2 = Aa x Aa (selfing F1 progenies)
F2 = AA, Aa, Aa, aa
As sickle cell anemia is an autosomal recessive disease thus the offspring with the genotype aa will be infected whereas the rest will be normal.
Hence,
The probability of diseased offspring (a) = 1/4
The probability of normal offspring (b) = 1 - 1/4 = 3/4
Now,
Applying the binomial theorem equation = n! / s! . t! x (a)s (b)t
= 7! / 3! . 4! x (1/4)3 . (3/4)4
= 7 x 6 x 5 x 4! x 1 x 1 x 1 x 3 x 3 x 3 x 3
3 x 2 x 1 x 4! x 4 x 4 x 4 x 4 x 4 x 4 x 4
= 2835 / 16384 = 0.173
Now, to for rounding of a number, if at the last deigit of 0.173 is less then 5 then that should be discarded.
Therefore, the answer is 0.17 (after rounding off to nearest hundredth).
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