logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Probability
0 votes

Lets say you enter a Chess tournament. The probability of winning a game against half the players is 0.3, the probability of winning against one quarter of them is 0.4 and the probability of winning against the remaining one quarter is 0.5. Let's say you play against a randomly chosen opponent. What is your probability of winning?

(A) 0.4

(B) 0.375

(C) 0.33

(D) 0.3

Can you answer this question?
 
 

1 Answer

0 votes
Let $A_i$ be the event of playing an opponent of type $i$.
$A_1$ = playing the half of the opponent pool where the probability of winning P (winning|$A_1$) = 0.3
$A_2$ = playing the half of the opponent pool type 2, where the probability of winning P (winning|$A_2$) = 0.4
$A_3$ = playing the half of the opponent pool type 3, where the probability of winning P (winning|$A_3$) = 0.5
By total probability theorem, we get, P(winning) = P($A_1$)P(winning|$A_1$) + P($A_2$)P(winning|$A_2$) + P($A_3$)P(winning|$A_3$)
P (winning) = 50% $\times$ 0.3 + 25% $\times$ 0.4 + 25% $\times$ 0.5
P (winning) = 0.375.
answered Feb 12, 2014 by balaji.thirumalai
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...