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The probability of winning is 0.44 .
<u>Step-by-step explanation:</u>
Here it's given that , You enter a chess tournament where your probability of winning a game is 0.3 against half the players (call them type 1), 0.4 against a quarter of the players (call them type 2), and 0.5 against the remaining quarter of the players (call them type 3). You play a game against a randomly chosen opponent. More precisely :
Now, we choose a random opponent and we need to find probability of winning which is possible as :
<u>1. player chosen from type1</u>
<u>2. player chosen from type2</u>
<u>3. player chosen from type3</u>
Combining all cases we get :
⇒
⇒
⇒
∴ The probability of winning is 0.44 .