3. Joanne is guessing which day in November is Bess's birthday. Joanne knows that Bess's birthday does not fall on an odd-numbered day. What is the probability that Joanne will guess the correct day on her first try?
3. Joanne is guessing which day in November is Bess's birthday. Joanne knows that Bess's birthday does not fall on an odd-numbered day. What is the probability that Joanne will guess the correct day on her first try?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![### Probability Question: Bess's Birthday in November
**Question:**
Joanne is guessing which day in November is Bess’s birthday. Joanne knows that Bess’s birthday does not fall on an odd-numbered day. What is the probability that Joanne will guess the correct day on her first try?
**Explanation:**
This question requires an understanding of the basic principles of probability, specifically in the context of determining the likelihood of an event, based on certain constraints.
**Calculations:**
1. **Total Days in November:** November has 30 days.
2. **Odd-Numbered Days:** The odd-numbered days in November are 1, 3, 5, ..., 29. There are 15 odd-numbered days (since every second day is odd).
3. **Even-Numbered Days:** With 30 total days and 15 odd-numbered days, the remaining 15 days are even-numbered.
Since Bess's birthday falls on an even-numbered day, Joanne has 15 possible days to choose from. Therefore, the probability that Joanne will guess the correct day on her first try is the ratio of the number of successful outcomes to the number of possible outcomes.
**Probability Calculation:**
\[ \text{Probability} = \frac{1}{\text{Number of even-numbered days}} = \frac{1}{15} \]
Therefore, the probability that Joanne will correctly guess Bess's birthday on the first try is \( \frac{1}{15} \) or approximately 6.67%.
### Additional Information:
Understanding how to calculate probabilities by narrowing down possibilities based on given information is a crucial skill in statistics and mathematics. This question illustrates how constraints (knowing the birthday is not on an odd-numbered day) can simplify a probability problem.
**Note:** There are no graphs or diagrams associated with this question.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58b49e45-0283-476e-ae82-98219e693dca%2Fab71906a-b8b5-4fef-af01-dbe442b64e36%2Fspbbcgr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Question: Bess's Birthday in November
**Question:**
Joanne is guessing which day in November is Bess’s birthday. Joanne knows that Bess’s birthday does not fall on an odd-numbered day. What is the probability that Joanne will guess the correct day on her first try?
**Explanation:**
This question requires an understanding of the basic principles of probability, specifically in the context of determining the likelihood of an event, based on certain constraints.
**Calculations:**
1. **Total Days in November:** November has 30 days.
2. **Odd-Numbered Days:** The odd-numbered days in November are 1, 3, 5, ..., 29. There are 15 odd-numbered days (since every second day is odd).
3. **Even-Numbered Days:** With 30 total days and 15 odd-numbered days, the remaining 15 days are even-numbered.
Since Bess's birthday falls on an even-numbered day, Joanne has 15 possible days to choose from. Therefore, the probability that Joanne will guess the correct day on her first try is the ratio of the number of successful outcomes to the number of possible outcomes.
**Probability Calculation:**
\[ \text{Probability} = \frac{1}{\text{Number of even-numbered days}} = \frac{1}{15} \]
Therefore, the probability that Joanne will correctly guess Bess's birthday on the first try is \( \frac{1}{15} \) or approximately 6.67%.
### Additional Information:
Understanding how to calculate probabilities by narrowing down possibilities based on given information is a crucial skill in statistics and mathematics. This question illustrates how constraints (knowing the birthday is not on an odd-numbered day) can simplify a probability problem.
**Note:** There are no graphs or diagrams associated with this question.
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