1. A person’s blood type is made up of a blood group (A, B, AB, O) and a Rhesus factor (R+, R−). If the blood group and Rhesus factor of an individual is classed as A and R+, respectively, then the blood type of the individual is labelled A+. The proportion for each combination of blood group and Rhesus factor in the population are conveniently expressed in the following joint probability table.a Table 1: Joint Probability Table Blood Group R+ R- A 0.28 0.10 B 0.06 0.06 AB 0.03 0.06 O 0.38 0.03 (a) What is the probability that a randomly chosen individual either has blood group B or has a positive Rhesus factor (or both)? (b) What is the probability that a randomly chosen individual either does not have blood group O or has a negative Rhesus factor (or both)? (c) What is the probability that a randomly chosen individual does not have blood group AB and has a negative Rhesus factor? (d) What is the probability that a randomly chosen individual has a negative Rhesus factor given that they do not have blood group B? (e) What is the probability that a randomly chosen individual has blood group A given that they have a positive Rhesus factor? (f) Are events blood group A and positive Rhesus factor independent? Explain.
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.
1. A person’s blood type is made up of a blood group (A, B, AB, O) and a Rhesus factor (R+, R−). If the blood group and Rhesus factor of an individual is classed as A and R+, respectively, then the blood type of the individual is labelled A+. The proportion for each combination of blood group and Rhesus factor in the population are conveniently expressed in the following joint
Table 1: Joint Probability Table
| Blood Group | R+ | R- |
| A | 0.28 | 0.10 |
| B | 0.06 | 0.06 |
| AB | 0.03 | 0.06 |
| O | 0.38 | 0.03 |
(a) What is the probability that a randomly chosen individual either has blood group B
or has a positive Rhesus factor (or both)?
(b) What is the probability that a randomly chosen individual either does not have blood group O or has a negative Rhesus factor (or both)?
(c) What is the probability that a randomly chosen individual does not have blood group AB and has a negative Rhesus factor?
(d) What is the probability that a randomly chosen individual has a negative Rhesus factor given that they do not have blood group B?
(e) What is the probability that a randomly chosen individual has blood group A given that they have a positive Rhesus factor?
(f) Are
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