Question 1201524: Kind of a big one:
Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor the B antigen is present, the letter O is used.
The following table gives the percent of a certain country's population having each of the eight possible blood types in the sample space. Note that the presence or absence of the Rh antigen is indicated by the symbols + or −, respectively.
Blood Types percentage: A+ is 35.7 A− is 6.3 B+ is 9.5 B− is 1.5 AB+ is 3.4 AB− is 0.8 O+ is 37.2 O− is 5.6
(a) What is the probability that a person selected randomly from the population has a blood type that is type O or Rh+?
(b) What is the probability that a person selected randomly from the population has a blood type that contains the A antigen?
(c) What is the probability that a person selected randomly from the population has a blood type that is type AB or Rh−?
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
Human blood is classified by the presence or absence of three main antigens (A, B, and Rh).
When a blood specimen is typed, the presence of the A and/or B antigen is indicated
by listing the letter A and/or the letter B.
If neither the A nor the B antigen is present, the letter O is used.
The following table gives the percent of a certain country's population
having each of the eight possible blood types in the sample space.
Note that the presence or absence of the Rh antigen is indicated
by the symbols + or −, respectively.
Blood Types percentage:
A+ is 35.7 A− is 6.3 B+ is 9.5 B− is 1.5 AB+ is 3.4 AB− is 0.8 O+ is 37.2 O− is 5.6
(a) What is the probability that a person selected randomly from the population
has a blood type that is type O or Rh+?
(b) What is the probability that a person selected randomly from the population
has a blood type that contains the A antigen?
(c) What is the probability that a person selected randomly from the population
has a blood type that is type AB or Rh−?
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Probably, persons with medical education read this table easily,
but for me it is better to rewrite and to present it in other form.
I will present this table horizontally with four upper lines of names
Line 1 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
Line 2 A+ | A- | B+ | B- | AB+ | AB- | O+ | O-
Line 3 ABR | ABR | ABR | ABR | ABR | ABR | ABR | ABR
Line 4 A R A BR B ABR AB R
Line 5 35.7 6.3 9.5 1.5 3.4 0.8 37.2 5.6
Line 1 simply numerates the columns of the table.
Line 2 is the standard medical designations of states.
Line 3 contains the format ABR, repeated 8 times in 8 columns
Line 4 shows the factual content (presence/absence) of three main antigens
(A, B, or Rh; for the last, I use R for simplicity)
Line 5 represents the given numbers.
I checked that the sum of numbers in Line 5 is 100, representing 100%.
It convinces me that the given info represents the disjoint states, that covers 100% space events.
(a) What is the probability that a person selected randomly from the population
has a blood type that is type O or Rh+?
To answer (a), add the numbers L(7), L(8), L(1), L(3), L(5) from Line 5.
37.2 + 5.6+ 35.7+ 9.5 + 3.4 = 91.4. ANSWER
Since you see from Line 2 or Line 4 that L(7) and L(8) are of type O; L(1), L(3), L(5) are of type Rh+.
(b) What is the probability that a person selected randomly from the population
has a blood type that contains the A antigen?
To answer (b), add the numbers L(1), L(2), L(5), L(6) from Line 5.
35.7+ 6.3 + 3.4 + 0.8 = 46.2. ANSWER
Since you see from Line 2 or Line 4 the presence of symbol "A" at these columns.
(c) What is the probability that a person selected randomly from the population
has a blood type that is type AB or Rh−?
To answer (c), add L(5), L(6), L(4), L(6), L(8) from Line 5.
(If you just got the idea, perform this calc on your own).
Since you see from Line 2 or Line 4 the presence of symbols "AB" or "-" at these columns.
Solved.
Evaluating this problem " in whole " according to its complexity level,
I'd say that it is quite stupid mechanical job.
To be honest, I do not understand why the tutors should do (or are expected to do) so primitive assignments.
In any case, I hope you do understand everything in this solution.
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After completing this task, I think what useful you can learn from it.
I think, THIS LESSON would be useful for you:
In every part, they ask you about the probability of the union of some disjoint events.
Such probability is always the sum of probabilities of participating events.
The key word here is "disjoint events".
Good to memorize.
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