Probability questions: (1 Viewer)

Show your work if possible. TIA

1.) A state lottery consists of selecting balls from four containers, each consisting of balls numbered 0-9. Suppose you win if any permutation of your chosen four numbers win. Find the probability of winning if the four digits you chose were:                                            
(a) 2, 3, 4, 5.                                                                    
(b) 2, 3, 4, 4.                                                                    
(c) 2, 2, 4, 4.                                                                                             
                                                                                     
 2. )Two friends choose to have a best of nine video game battle with the winner being the first player to win five times. A possible outcome would be BBABAABB where player A wins the3rd, 5th and 6th games while player B wins games 1,2,4,7, and 8. There is no 9th game because player B has already won 5 times. How many different orders are possible if the battle goes    
 (a) 6 games?                                                                 
 (b) 9 games?                                                                 
                                                                                      
 3.) At the end of the semester, 20 students fill out a class evaluation for a professor. They can rank him on a scale of 1-5, where 1 is terrible and 5 is excellent. How many different ratings combinations are possible?

Ben & Jerry's said:

Show your work if possible. TIA

1.) A state lottery consists of selecting balls from four containers, each consisting of balls numbered 0-9. Suppose you win if any permutation of your chosen four numbers win. Find the probability of winning if the four digits you chose were:                                            
(a) 2, 3, 4, 5.                                                                    
(b) 2, 3, 4, 4.                                                                    
(c) 2, 2, 4, 4.     

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Quick takes on the first two questions...

a) 0.0024

b) 0.0012

c) 0.0006

Repeating digits gives you fewer permutations to win with. 

Ben & Jerry's said:

2. )Two friends choose to have a best of nine video game battle with the winner being the first player to win five times. A possible outcome would be BBABAABB where player A wins the3rd, 5th and 6th games while player B wins games 1,2,4,7, and 8. There is no 9th game because player B has already won 5 times. How many different orders are possible if the battle goes    
 (a) 6 games?                                                                 
 (b) 9 games?                                                                 

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a) 10.  If they play 6 games and one player wins 5 of them, the other player loses just 1.  There are five possible choices for the 1 he loses (he can't have lost the sixth game, because it would have already ended).  Either player could be the one to lose, so we double it to get 10. 

b) 140. There are (8 choose 4) = 70 different ways for the first 8 games to be split 4-4.  For each of those, there are two possible outcomes in the 9th game, so 70 x 2 = 140.

Will take a stab at #3 in a bit.  

Ben & Jerry's said:

 3.) At the end of the semester, 20 students fill out a class evaluation for a professor. They can rank him on a scale of 1-5, where 1 is terrible and 5 is excellent. How many different ratings combinations are possible?

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Don't have a simple explanation this one but I figure it's just sampling 5 objects with replacement 20 times, and an online calculator tells me there are 10,626 possible combinations for that.    

1) 50%

2) 50%

-5^2

So did I get them right?

Ignoratio Elenchi said:

-5^2

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I've changed my opinion on this over the years.  I was originally strongly in favor of 25 but now I'm cool with -25.

I was told there would be no math.

It's 50/50, you either win the lottery or you don't.