Question

finding probabilities

every person has blood type o, a, b, or ab. a random group of people are blood-typed, and the results are shown in the table.

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$$\begin{array}{|c|c|} \\hline \\text{blood type} & \\text{number of people} \\\\ \\hline \\text{o} & 22 \\\\ \\hline \\text{a} & 20 \\\\ \\hline \\text{b} & 6 \\\\ \\hline \\text{ab} & 2 \\\\ \\hline \\end{array}$$

use the table to determine the following probabilities:
the probability that a randomly chosen person from this group has type b is dropdown
the probability that a randomly chosen person from this group has type ab is dropdown
the probability that a randomly chosen person from this group has type b or type ab blood is dropdown

Explanation:

Calculate the total sample space

Using the Sample Space knowledge point

$$ \text{Total People} = 22 + 20 + 6 + 2 = 50 $$

Find the probability of type B blood

Using the Theoretical Probability and Favorable Outcomes knowledge points

$$ P(\text{Type B}) = \frac{6}{50} = \frac{3}{25} = 0.12 $$

Find the probability of type AB blood

Using the Theoretical Probability and Favorable Outcomes knowledge points

$$ P(\text{Type AB}) = \frac{2}{50} = \frac{1}{25} = 0.04 $$

Find the probability of type B or type AB blood

Using the Mutually Exclusive Events and Probability Addition Rule knowledge points

$$ P(\text{Type B or Type AB}) = P(\text{Type B}) + P(\text{Type AB}) = \frac{6}{50} + \frac{2}{50} = \frac{8}{50} = \frac{4}{25} = 0.16 $$

Answer:

Question 1

The probability that a randomly chosen person from this group has type B is <blank>\(\frac{3}{25}\)</blank> (or <blank>\(0.12\)</blank>).

Question 2

The probability that a randomly chosen person from this group has type AB is <blank>\(\frac{1}{25}\)</blank> (or <blank>\(0.04\)</blank>).

Question 3

The probability that a randomly chosen person from this group has type B or type AB blood is <blank>\(\frac{4}{25}\)</blank> (or <blank>\(0.16\)</blank>).