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. What is the probability of winning

The probability of winning is 0.44 .

Step-by-step explanation:

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 :

1. player chosen from type1

2. player chosen from type2

3. player chosen from type3

Combining all cases we get :

⇒

⇒

⇒

∴ The probability of winning is 0.44 .

the slope of the first function is -3. (3/1)

the slope of the second function is 1. (13-10/6-3).

since |-3| is greater than |1|, the function with the steepest slope is the first.

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