Sickle Cell Anemia Sickle cell anemia is a genetic blood disorder where red blood cells lose their flexibility and assume an abnormal, rigid, sickle shape, which results in a risk of various complications. If both parents are carriers of the disease, then a child has a 25% chance of having the disease, 50% chance of being a carrier, and 25% chance of neither having the disease nor being a carrier. If two parents who are carriers of the disease have 6 children, what is the probability that: (a) 0 will have the disease? (b) 5 will have the disease? (c) at least 2 will neither have the disease nor be a carrier? (d) the first child with the disease will be child number 1?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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We have,
n = 6
p1 = probability that the child has disease = 25% = 0.25
p2 = probability that the child will be a carrier of the disease = 50% = 0.50
p3 = probability that the child neither will be a carrier of the disease nor will have the disease = 25% = 0.25
Part a:
Let X denote the number of children that will have the disease.
Thus, X~B(n = 6, p1 =0.25)
The probability that 0 will have the disease is computed as,
Thus, the probability that 0 will have the disease is 0.1780.
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