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
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
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F966de6a6-a059-4e5f-a825-6f19603bce12%2Fb837f542-9503-4ef6-b99d-79a8651a8162%2Fgn8q8ym_processed.png&w=3840&q=75)
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.
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