Answer to Question #115979 in Statistics and Probability for Ghost

Question #115979

An expert backgammon player is currently competing in two tournaments. He estimates the probability of winning the first tournament as 0.6 and the probability of winning the second tournament as 0.5. If he wins the first tournament, he estimates the probability of winning the second tournament increases to 0.65 because of an increase in confidence. What is the probability of:
(i) the player winning both tournaments?

(ii) the player winning at least one tournament?

Expert's answer

(i) the player winning both tournaments:

P=P(winning I tournament)*P(winning II tournament after winning I tournament)=0.6*0.65=0.39

(ii) the player winning at least one tournament:

P=1- P(lose I tour. and lose II tour.)=1- (1-0.6)*(1-0.5)=1-0.2=0.8=80%