Question

In addition to being grouped into four types, human blood is grouped by its Rhesus (Rh) factor. Consider the figures below that show the distribution of these groups of Americans.

O A B AB
Rh+ 37% 34% 10% 4%
Rh- 6% 6% 2% 1%
Choose i American at random. Find the probability that the chosen person: a. Has type B negative blood. Has type B blood, given that the person is Rh-.
b. C. Has B+ or A-blood. Select one or more U 0.02 0.16 0.121 0 0.054 0.155 0.133

Answer 1

a. The probability that a randomly chosen American has type B negative blood is 0.06, or 6%.

b. The probability that a randomly chosen American has type B blood given that the person is Rh- is 0.16, or 16%.

Step-by-step explanation:

In the given distribution, for part (a), we look at the intersection of the "B" row and the "Rh-" column, which corresponds to type B negative blood. The probability is calculated by multiplying the percentages: 0.06 (6%).

For part (b), we are asked to find the probability of having type B blood given that the person is Rh-. This is obtained by considering the "B" row and the "Rh-" column and dividing the percentage of B Rh- individuals by the total percentage of Rh- individuals. In this case, it is 0.16 (16%).

In summary, probabilities are calculated by understanding the relationships between the categories. For part (a), it's the probability of having type B negative blood, and for part (b), it's the conditional probability of having type B blood given that the person is Rh-. These calculations provide insights into the likelihood of specific blood types within the American population, considering both ABO types and the Rh factor.

Answer 2

The probability of a randomly chosen American having B negative blood is 2%. If the person is already known to be Rh-, the probability of them having B blood is 25%. The probability of an American having B+ or A- blood is 16%.

Step-by-step explanation:

The probability that the chosen person has type B negative blood is given directly in the figures as 2%. This represents the proportion of Americans with this blood type.

To find the probability that a person has type B blood, given that the person is Rh-, we use conditional probability. The figures show that 8% of Americans are Rh- (sum of all Rh-), and of these, 2% have type B blood. Therefore, the probability of having type B blood when already knowing the person is Rh- is calculated by the formula P(B | Rh-) = P(B AND Rh-) / P(Rh-), which gives 2% / 8% = 0.25 or 25%.

For those with B+ or A- blood, we simply add the percentages for B+ (10%) and A- (6%), which yields a probability of 16%.