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avatar+1836 

My basketball team has eight games next month. We're pretty good; we have a 2/3 chance to win in each game. What is the probability we have a winning streak of at least four games at some point during the month?

 May 15, 2015

Best Answer 

 #3
avatar+118696 
+13

 

1 2 3 4 5 6 7 8  FOUR IN A ROW
W W W L            2×(23)4×(13)=32243=0.1316872427983539
      L W W W W
L W W W W L           3×(23)4×(13)2=16243=0.065843621399177
  L W W W W L  
    L W W W W L

 

 

1 2 3 4 5 6 7 8                          FIVE IN A ROW
W W W W  L          2×(23)5×(13)=64729=0.0877914951989026
     L W W W W W
L W W W W W  L       2×(23)5×(13)2=642187=0.0292638317329675      
  L W W W W W  L

 

 

1 2 3 4 5 6 7 8                       SIX IN A ROW
W W W W  W  L        2×(23)6×(13)=1282187=0.0585276634659351
   L  W W W W W W
L W W W W W  W  L     (23)6×(13)2=646561=0.0097546105776558

 

1 2 3 4 5 6 7 8    SEVEN IN A ROW
W W W W W W W L  
L W W W W W W W  

 

 

I TRIED TO PUT ALL THIS INTO A TABLE BUT THE TABLE DID NOT COPE VERY WELL   

 

FOUR IN A ROW

 

2×(23)4×(13)=32243=0.1316872427983539

 

3×(23)4×(13)2=16243=0.065843621399177

 

FIVE IN A ROW

 

2×(23)5×(13)=64729=0.0877914951989026

 

2×(23)5×(13)2=642187=0.0292638317329675

 

SIX IN A ROW

 

2×(23)6×(13)=1282187=0.0585276634659351

 

(23)6×(13)2=646561=0.0097546105776558

 

SEVEN IN A ROW  

 

2×(23)7×(13)=2566561=0.0390184423106234

 

EIGHT IN A ROW

 

(23)8=2566561=0.0390184423106234

 

 

32243+16243+64729+642187+1282187+646561+2566561+2566561=112243=0.4609053497942387

 May 17, 2015
 #1
avatar+130466 
+3

 

Probabilty of a winning streak of 4 = (2/3)^4  = 16/81

Probabilty of a winning streak of 5 = (2/3)^5  = 32/243

Probabilty of a winning streak of 6 = (2/3)^6  = 64/729

Probabilty of a winning streak of 7 = (2/3)^7  = 128/2187

Probabilty of a winning streak of 8 = (2/3)^8  = 256/6561

 

So the total probability of winning four or more in a row is

16 / 81 + 32 / 243 + 64 / 729 + 128 / 2187 + 256 / 6561   = 3376 / 6561  = about 51.46%

 

 

 May 15, 2015
 #2
avatar+118696 
+7

I am sure it is not that simple Chris  

 May 17, 2015
 #3
avatar+118696 
+13
Best Answer

 

1 2 3 4 5 6 7 8  FOUR IN A ROW
W W W L            2×(23)4×(13)=32243=0.1316872427983539
      L W W W W
L W W W W L           3×(23)4×(13)2=16243=0.065843621399177
  L W W W W L  
    L W W W W L

 

 

1 2 3 4 5 6 7 8                          FIVE IN A ROW
W W W W  L          2×(23)5×(13)=64729=0.0877914951989026
     L W W W W W
L W W W W W  L       2×(23)5×(13)2=642187=0.0292638317329675      
  L W W W W W  L

 

 

1 2 3 4 5 6 7 8                       SIX IN A ROW
W W W W  W  L        2×(23)6×(13)=1282187=0.0585276634659351
   L  W W W W W W
L W W W W W  W  L     (23)6×(13)2=646561=0.0097546105776558

 

1 2 3 4 5 6 7 8    SEVEN IN A ROW
W W W W W W W L  
L W W W W W W W  

 

 

I TRIED TO PUT ALL THIS INTO A TABLE BUT THE TABLE DID NOT COPE VERY WELL   

 

FOUR IN A ROW

 

2×(23)4×(13)=32243=0.1316872427983539

 

3×(23)4×(13)2=16243=0.065843621399177

 

FIVE IN A ROW

 

2×(23)5×(13)=64729=0.0877914951989026

 

2×(23)5×(13)2=642187=0.0292638317329675

 

SIX IN A ROW

 

2×(23)6×(13)=1282187=0.0585276634659351

 

(23)6×(13)2=646561=0.0097546105776558

 

SEVEN IN A ROW  

 

2×(23)7×(13)=2566561=0.0390184423106234

 

EIGHT IN A ROW

 

(23)8=2566561=0.0390184423106234

 

 

32243+16243+64729+642187+1282187+646561+2566561+2566561=112243=0.4609053497942387

Melody May 17, 2015
 #4
avatar+1836 
+1

Thank you both, but Melody's answer was correct. Thanks guys so so much once again!!

 May 17, 2015

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