Brian and Jennifer are planning to get married at the end of the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type. Suppose a recent study shows that 29% of adults have blood type A, 35% of adults have blood type B, 24% of adults have blood type AB, and 12% of adults have blood type O. The tree diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question
Brian and Jennifer are planning to get married at the end of the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type.

Suppose a recent study shows that 29% of adults have blood type A, 35% of adults have blood type B, 24% of adults have blood type AB, and 12% of adults have blood type O. The tree diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities.

**Tree Diagram Explanation:**

The tree diagram is divided into two main branches for Brian's blood type, labeled A, B, AB, and O with probabilities of 0.29, 0.35, 0.24, and 0.12 respectively. Each of these branches further splits into four branches showing the possible blood types for Jennifer (A, B, AB, O), again with the same probabilities (0.29, 0.35, 0.24, 0.12). 

The branches represent the joint probabilities of each combination of blood types for Brian and Jennifer. To find the probability that they have the same blood type, we sum the probabilities along the branches where Brian’s blood type matches Jennifer’s.

- Probability both have blood type A: 0.29 (Brian) * 0.29 (Jennifer) = 0.0841
- Probability both have blood type B: 0.35 (Brian) * 0.35 (Jennifer) = 0.1225
- Probability both have blood type AB: 0.24 (Brian) * 0.24 (Jennifer) = 0.0576
- Probability both have blood type O: 0.12 (Brian) * 0.12 (Jennifer) = 0.0144

The total probability that Brian and Jennifer have the same blood type is the sum of these probabilities:

\[ P\text{(Brian and Jennifer have the same blood type)} = 0.0841 + 0.1225 + 0.0576 + 0.0144 \]

Finally, give the total probability as a decimal, precise to at least two decimal places.
Transcribed Image Text:Brian and Jennifer are planning to get married at the end of the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type. Suppose a recent study shows that 29% of adults have blood type A, 35% of adults have blood type B, 24% of adults have blood type AB, and 12% of adults have blood type O. The tree diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities. **Tree Diagram Explanation:** The tree diagram is divided into two main branches for Brian's blood type, labeled A, B, AB, and O with probabilities of 0.29, 0.35, 0.24, and 0.12 respectively. Each of these branches further splits into four branches showing the possible blood types for Jennifer (A, B, AB, O), again with the same probabilities (0.29, 0.35, 0.24, 0.12). The branches represent the joint probabilities of each combination of blood types for Brian and Jennifer. To find the probability that they have the same blood type, we sum the probabilities along the branches where Brian’s blood type matches Jennifer’s. - Probability both have blood type A: 0.29 (Brian) * 0.29 (Jennifer) = 0.0841 - Probability both have blood type B: 0.35 (Brian) * 0.35 (Jennifer) = 0.1225 - Probability both have blood type AB: 0.24 (Brian) * 0.24 (Jennifer) = 0.0576 - Probability both have blood type O: 0.12 (Brian) * 0.12 (Jennifer) = 0.0144 The total probability that Brian and Jennifer have the same blood type is the sum of these probabilities: \[ P\text{(Brian and Jennifer have the same blood type)} = 0.0841 + 0.1225 + 0.0576 + 0.0144 \] Finally, give the total probability as a decimal, precise to at least two decimal places.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Data Collection, Sampling Methods, and Bias
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman