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The Boomtown Bears are playing against the Tipton Toros in a baseball tournament. The winner of the tournament is the first team that wins three games. The Bears have a probability of 1/5 of winning each game. Find the probability that the Bears win the tournament.

 Jan 10, 2023
 #1
avatar+34 
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Well, if there is only 3 games, and 1/5 probability for each, I believe you just do:

1/5 * 1/5 * 1/5

= 1/125 probability that the Bears actually win the tournament.

 

However, if I am wrong, please tell me, as I would be happy to learn what my mistake was and how I could have corrected it!

 Jan 11, 2023
 #4
avatar+118196 
+1

Nice try Mmm but you forgot some of the posibilities   wink

 

The Boomtown Bears are playing against the Tipton Toros in a baseball tournament. The winner of the tournament is the first team that wins three games. The Bears have a probability of 1/5 of winning each game. Find the probability that the Bears win the tournament.

I will assume that it is imposible to draw.

 

P(B wins) = 1/5

 

P(B wines 3 games out of 3) =    1/   5^3                                                      =  25 / 5^5

 

P(B wins 3 games out of 4) =  4C3 * (1/5)^3 * (4/5) = 4 * 4 / 5^4 = 16 / 5^4  =  80 / 5^5

 

P ( B wins 3 games out of 5)  =  5C3 * (1/5)^3 *( 4/5)^2 = 10 *  16 /  5^5      =   160 / 5^5

 

add them together    25+80+160 = 265

 

265 /  5^5  simplifies to   53/625  =  0.0848

 

So the prob that the bears win is  8.48%

 Jan 14, 2023

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