[BruceZ]

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1st Question:
This question is stupid. Let's say you are a 1/6 shot to pull a red marble out of a bag of 5 blue marbles and 1 red marble. What are the odds you pull at least one red marble out if you get two tries. So, you draw the first try. IF you get a red marble, you don't need to do the second trial - you already got your red marble. If you don't draw a red marble, you replace your blue marble into the bag and redraw. Are the chances you draw a red marble if you draw two times just 2/6 = 1/3?

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No. 1/6 + (5/6)*(1/6) =~ 30.6%

Or 1 - (5/6)*(5/6) =~ 30.6%.


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2nd Question:
This is a question I would love to have answered. I would love the formula if possible also. Let's say you have a quarter. The most probable outcome, if you flip it ten times, is 5 heads and 5 tails. However, what are the odds that this actually happens.

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C(10,5)*(1/2)^5*(1/2)^5 =~ 24.6%.

C(10,5) is the number of ways to pick the 5 heads, and is equal to 10*9*8*7*6/(5*4*3*2*1).


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A similar situation: You have a quarter. You flip it 100 times. What are the odds you land 60 heads and 40 tails

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C(100,60)*(1/2)^60*(1/2)^40 =~ 1.1%