I solve this question with further steps which was not so much necessary, but it's correct
Answer fast ..................
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Answer:
There are three kind of beta-thalassemia.
Total possible outcome= 3 types of beta- thalassemia + 1 [child will have no trace of disease] = 4
As we know Probability(outcome) =
Probability that the child will have beta-thalassemia major =\frac{_{1}^{3}\textrm{C}}{_{1}^{4}\textrm{C}}
=
∴ favorable=
And , Total =
Probability that the child will have no trace of the disease=
Note that 
in the given closed interval, so the area is exactly given by the definite integral
(no absolute values needed!)
Integrating gives
(no absolute values needed!)
Integrating gives