Is the Book's Answer Accurate?

  • Thread starter davedave
  • Start date
Or more precisely, eat it and then have it again. :-)In summary, the problem involves a jar of 100 jellybeans with 80 green and 20 yellow jellybeans. 10 jellybeans are selected and the question is what is the probability that there are at least 6 green jellybeans. The solution involves using the binomial distribution and the binomcdf function on a TI 84 calculator. The probability of getting at most 5 green jellybeans is calculated and then subtracted from 1 to get the final answer of 0.967. However, it is noted that this answer does not match the given answer of 0.975, suggesting a possible error in the book's answer. Additionally, the problem
  • #1
davedave
50
0
In a jar of 100 jellybeans, there are 80 green and 20 yellow jellybeans. 10 jellybeans are selected. What is the probability that there are at least 6 green jellybeans?

(book's answer 0.975)

This is my solution. The probability for getting a green one is .08 and for getting a yellow one is 0.2.

So, we can use the binomial distribution for solving this problem. The success refers to a green jellybean and the failure represents the non-green jellybean.

We can use the function, binomcdf, on the TI 84 calculator to work out the answer.

The probability of getting AT MOST 5 green jellybeans is binomcdf(10,0.8,5)

So, to solve the problem, we do 1-binomcdf(10.0.8,5)=0.967.

That doesn't match the answer. Is the book's answer, 0.975, wrong?
 
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  • #2
The probability that the first jellybean selected is green is 80%. There are 99 jelly beans left. What is the probability that the second jelly bean is green on the condition that the first jelly bean is green??
 
  • #3
In other words, this is NOT a binomial distribution. Binomial distribution apply to sampling with replacement. This is sampling without replacement.
 
  • #4
Phrak and Halls, you are both assuming that the jelly beans are selected without replacement, but this is not stated in the OP.
In a jar of 100 jellybeans, there are 80 green and 20 yellow jellybeans. 10 jellybeans are selected. What is the probability that there are at least 6 green jellybeans?
The problem as stated doesn't say anything about how they are selected.

davedave,
Did you post the exact wording of the problem?
 
  • #5
Mark44 said:
Phrak and Halls, you are both assuming that the jelly beans are selected without replacement, but this is not stated in the OP.

The problem as stated doesn't say anything about how they are selected.

Yes it does. 10 beans are selected, rather than 10 selections made. The count is attributed to jelly beans, not selections. Nice try, though.
 
  • #6
To say that 10 beans are selected doesn't rule out, IMO, the possibility that they were selected one at a time, either with or without replacement. If you can find a definition of the verb "to select" that backs up your interpretation, I will gladly change my mind.
 
  • #7
So if I give you a dollar, take it back, give the same dollar to you, take it back and repeat that 8 more times, I have given you ten dollars? I'll have to try that when I go shopping tomorrow!
 
  • #8
I would say that you gave me one dollar. But if your wallet had a hundred dollar bills in it, and you pulled one out, gave it to me, took it back, pulled another one out of your wallet, gave it to me, took it back, etc., then I would say that you gave me ten dollars. Even if I ended up with no more money than what I had started with.
 
  • #9
Mark44 said:
I would say that you gave me one dollar. But if your wallet had a hundred dollar bills in it, and you pulled one out, gave it to me, took it back, pulled another one out of your wallet, gave it to me, took it back, etc., then I would say that you gave me ten dollars. Even if I ended up with no more money than what I had started with.

You want to have your jelly bean and eat it too.
 

Related to Is the Book's Answer Accurate?

1) Is it possible for a book's answer to be wrong?

Yes, it is possible for a book's answer to be wrong. While books are typically written and reviewed by experts in their field, they are not infallible and can contain errors. It is important to critically evaluate the information presented in a book and verify it with other reliable sources.

2) How can I tell if a book's answer is wrong?

There are a few ways to determine if a book's answer is wrong. One way is to compare it with information from other reputable sources. If the answer disagrees with the majority of sources, it is likely incorrect. Another way is to conduct your own research and experiments to test the answer's validity. Additionally, if the answer seems illogical or contradicts known facts, it may be incorrect.

3) What should I do if I think a book's answer is wrong?

If you believe a book's answer is wrong, it is important to gather evidence to support your claim. This can include information from other sources, your own research, or logical reasoning. Once you have gathered evidence, you can contact the author or publisher to bring attention to the potential error. You can also share your findings with others to prevent them from being misled by the incorrect answer.

4) Can a book's answer be partially wrong?

Yes, a book's answer can be partially wrong. It is possible for a book to contain some accurate information but also have some incorrect or outdated information. It is important to critically evaluate the entire answer and not just accept it as completely correct without verifying it.

5) Why do books sometimes have wrong answers?

There are a variety of reasons why a book may have wrong answers. One possibility is that the author made a mistake during the writing or editing process. Another reason could be that new information has emerged since the book was published, rendering the answer outdated. It is also possible that the author or publisher has a bias that influenced the answer. Regardless of the reason, it is important to always critically evaluate the information presented in a book.

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