Is the Book's Answer Accurate?

[davedave]

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?

 

[Phrak]

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??

 

[HallsofIvy]

In other words, this is NOT a binomial distribution. Binomial distribution apply to sampling with replacement. This is sampling without replacement.

 

[Mark44]

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?

 

[Phrak]

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.

 

[Mark44]

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.

 

[HallsofIvy]

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!

 

[Mark44]

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.

 

[Phrak]

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.