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 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 A+ A− B+ B− AB+ AB− O+ O− Percent 35.7 6.1 9.5 1.5 3.4 0.8 37.4 5.6 (a) What is the probability that a person selected at random from the population has a blood type that is type A given that the person is Rh−? (Round your answer to two decimal places.) (b) What is the probability that a person selected at random from the population has a blood type that is Rh+ given that the person is type B? (Round your answer to two decimal places.)
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 country's population having each of the eight possible blood types in the
| Blood Types | A+ | A− | B+ | B− | AB+ | AB− | O+ | O− |
|---|---|---|---|---|---|---|---|---|
| Percent | 35.7 | 6.1 | 9.5 | 1.5 | 3.4 | 0.8 | 37.4 | 5.6 |
(b) What is the probability that a person selected at random from the population has a blood type that is Rh+ given that the person is type B? (Round your answer to two decimal places.)
(a) To find the probability that a person selected at random from the population has blood type A given that the person is Rh-, we need to use Bayes' theorem:
P(A|R-) = P(R-|A)P(A) / P(R-)
where P(A) is the probability of having blood type A, P(R-|A) is the probability of being Rh- given that the person has blood type A, and P(R-) is the probability of being Rh-.
From the table, we know that the percentage of people with blood type A- is 6.1%, and the percentage of people with Rh- is 8.9% (the sum of the percentages for A- and O-). The percentage of people with A- and Rh- can be found by multiplying the two percentages:
P(R-|A)P(A) = 6.1% x 6.1% = 0.003721
To find P(R-), we need to add up the percentages of people with A- and O-:
P(R-) = 6.1% + 5.6% = 11.7%
Now we can plug in the values into Bayes' theorem:
P(A|R-) = (0.003721) / (0.117) ii = 0.0318
Therefore, the probability that a person selected at random from the population has blood type A given that the person is Rh- is 0.0318, or about 3.18%.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
