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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.
use the table to determine the following probabilities.
the probability that a randomly chosen person from this group has type b is
the probability that a randomly chosen person from this group has type ab is
the probability that a randomly chosen person from this group has type b or type ab blood is
| blood type | number of people |
|---|---|
| a | 20 |
| b | 6 |
| ab | 2 |
To solve these probability problems, we first need to find the total number of people in the group. Then we can use the formula for probability: \( P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).
Step 1: Calculate the total number of people
We sum up the number of people for each blood type:
\[
22 + 20 + 6 + 2 = 50
\]
Probability of type B
Step 1: Identify favorable and total outcomes
- Number of people with type B: \( 6 \)
- Total number of people: \( 50 \)
Step 2: Calculate the probability
\[
P(\text{Type B}) = \frac{6}{50} = \frac{3}{25} = 0.12
\]
Probability of type AB
Step 1: Identify favorable and total outcomes
- Number of people with type AB: \( 2 \)
- Total number of people: \( 50 \)
Step 2: Calculate the probability
\[
P(\text{Type AB}) = \frac{2}{50} = \frac{1}{25} = 0.04
\]
Probability of type B or type AB
Step 1: Identify favorable and total outcomes
- Number of people with type B or AB: \( 6 + 2 = 8 \)
- Total number of people: \( 50 \)
Step 2: Calculate the probability
\[
P(\text{Type B or AB}) = \frac{8}{50} = \frac{4}{25} = 0.16
\]
Final Answers
- The probability that a randomly chosen person from this group has type B is \(\boldsymbol{\frac{3}{25}}\) (or \(0.12\)).
- The probability that a randomly chosen person from this group has type AB is \(\boldsymbol{\frac{1}{25}}\) (or \(0.04\)).
- The probability that a randomly chosen person from this group has type B or type AB blood is \(\boldsymbol{\frac{4}{25}}\) (or \(0.16\)).
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To solve these probability problems, we first need to find the total number of people in the group. Then we can use the formula for probability: \( P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).
Step 1: Calculate the total number of people
We sum up the number of people for each blood type:
\[
22 + 20 + 6 + 2 = 50
\]
Probability of type B
Step 1: Identify favorable and total outcomes
- Number of people with type B: \( 6 \)
- Total number of people: \( 50 \)
Step 2: Calculate the probability
\[
P(\text{Type B}) = \frac{6}{50} = \frac{3}{25} = 0.12
\]
Probability of type AB
Step 1: Identify favorable and total outcomes
- Number of people with type AB: \( 2 \)
- Total number of people: \( 50 \)
Step 2: Calculate the probability
\[
P(\text{Type AB}) = \frac{2}{50} = \frac{1}{25} = 0.04
\]
Probability of type B or type AB
Step 1: Identify favorable and total outcomes
- Number of people with type B or AB: \( 6 + 2 = 8 \)
- Total number of people: \( 50 \)
Step 2: Calculate the probability
\[
P(\text{Type B or AB}) = \frac{8}{50} = \frac{4}{25} = 0.16
\]
Final Answers
- The probability that a randomly chosen person from this group has type B is \(\boldsymbol{\frac{3}{25}}\) (or \(0.12\)).
- The probability that a randomly chosen person from this group has type AB is \(\boldsymbol{\frac{1}{25}}\) (or \(0.04\)).
- The probability that a randomly chosen person from this group has type B or type AB blood is \(\boldsymbol{\frac{4}{25}}\) (or \(0.16\)).