How do I approach these problems? Probability

AI Thread Summary
The discussion centers on two probability problems involving marbles and coin tosses. The first problem requires calculating the probability of drawing two red marbles from a shoebox after transferring marbles from a cookie jar. The second problem involves determining the probability that the number of heads exceeds the number of tails when a fair coin is tossed an even number of times. Participants discussed relevant concepts such as conditional probability and Bayes' Theorem to approach these problems. The thread was moved to the homework forums due to its nature as a textbook-style exercise.
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I have the following two problems and I don't know how to approach them.

A cookie jar has 3 red marbles and 1 white marble. A shoebox has 1 red marble and 1 white marble. Three marbles are chosen at random without replacement from the cookie jar and placed in the shoebox. Then 2 marbles are chosen at random without replacement from the shoebox. What is the probability that both marbles from the shoebox are red?

A fair coin is tossed n times, where n is an even integer. What is the probability that the number of heads exceeds the number of tails?

We talked about payoffs, Simple and Compound Growth,Conditional Probability, Law of total probability, Baye's Theorem. Simple math is obviously not enough, I need to prove it using those topics we covered. I'm not quite sure how to approach those problems. Any input?
Thank you
 
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Is this homework?
 
Moderator's note: thread moved to homework forums.
 
No...
 
Please allow me to clarify something from our forum guidelines:

... homework assignments or textbook style exercises for which you are seeking assistance are to be posted in the appropriate forum in our Homework & Coursework Questions area--not in blogs, visitor messages, PMs, or the main technical forums. This should be done whether the problem is part of one's assigned coursework or just independent study.

Since this is a textbook-style exercise, I moved it to the homework forums. Sorry if this created any confusion.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

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