Blood types All human blood can be typed as one of O, A, B, or AB, but the distribution of the t

Name: Problem 45, Chapter 5: The Practice of Statistics for AP
Uploaded: 2022-04-05T21:24:11-08:00
Duration: 1 min 55 s
Channel: Sheryl Ezze

step 1 So we have a probability distribution for blood types. And let me click write that up here. And

Question

Blood types All human blood can be typed as one of $\mathrm{O}, \mathrm{A}, \mathrm{B},$ or $\mathrm{AB},$ but the distribution of the types varies a bit with race. Here is the distribution of the blood type of a randomly chosen black American: $$\begin{array}{lcccc}\hline \text { Blood type: } & 0 & \mathrm{~A} & \mathrm{~B} & \mathrm{AB} \\\text { Probability: } & 0.49 & 0.27 & 0.20 & ? \\\hline\end{array}$$ (a) What is the probability of type $A B$ blood? Why? (b) What is the probability that the person chosen does not have type $A B$ blood? (c) Maria has type $\mathrm{B}$ blood. She can safely receive blood transfusions from people with blood types $\mathrm{O}$ and $\mathrm{B}$. What is the probability that a randomly chosen black American can donate blood to Maria?

   Blood types All human blood can be typed as one of $\mathrm{O}, \mathrm{A}, \mathrm{B},$ or $\mathrm{AB},$ but the distribution of the types varies a bit with race. Here is the distribution of the blood type of a randomly chosen black American: 
$$\begin{array}{lcccc}\hline \text { Blood type: } & 0 & \mathrm{~A} & \mathrm{~B} & \mathrm{AB} \\\text { Probability: } & 0.49 & 0.27 & 0.20 & ? \\\hline\end{array}$$
(a) What is the probability of type $A B$ blood? Why?
(b) What is the probability that the person chosen does not have type $A B$ blood?
(c) Maria has type $\mathrm{B}$ blood. She can safely receive blood transfusions from people with blood types $\mathrm{O}$ and $\mathrm{B}$. What is the probability that a randomly chosen black American can donate blood to Maria?

The Practice of Statistics for AP

Daren S. Starnes,… 5th Edition

Chapter 5, Problem 45

Instant Answer

Solved by Expert Sheryl Ezze

04/05/2022

Step 1

So, to find the probability of type AB blood, we subtract the sum of the probabilities of the other blood types from 1. This gives us $1 - (0.49 + 0.27 + 0.20) = 0.04$. Show more…

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Blood types All human blood can be typed as one of $\mathrm{O}, \mathrm{A}, \mathrm{B},$ or $\mathrm{AB},$ but the distribution of the types varies a bit with race. Here is the distribution of the blood type of a randomly chosen black American: $$\begin{array}{lcccc}\hline \text { Blood type: } & 0 & \mathrm{~A} & \mathrm{~B} & \mathrm{AB} \\\text { Probability: } & 0.49 & 0.27 & 0.20 & ? \\\hline\end{array}$$ (a) What is the probability of type $A B$ blood? Why? (b) What is the probability that the person chosen does not have type $A B$ blood? (c) Maria has type $\mathrm{B}$ blood. She can safely receive blood transfusions from people with blood types $\mathrm{O}$ and $\mathrm{B}$. What is the probability that a randomly chosen black American can donate blood to Maria?

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Key Concepts

Total Probability Principle

This principle asserts that the sum of the probabilities of all mutually exclusive outcomes of a random experiment must equal 1. It is used to determine unknown probabilities when the others in the distribution are known.

Complementary Probability

The concept of complementary probability states that the probability of an event not occurring is equal to 1 minus the probability that it does occur. It is a simple yet powerful tool for solving problems where the probability of a specific outcome is easier computed by subtracting from 1.

Addition Rule for Mutually Exclusive Events

When events cannot occur at the same time, they are mutually exclusive. The addition rule allows us to find the probability that either one of multiple mutually exclusive events occurs by simply summing the individual probabilities of each event.

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