Probability of winning a game of soccer, given 1 of the 10 players is Messi, is = 0.8. Probability of winning the same game, given 1 of the 10 players is Ronaldo is = 0.6. What is the probability of winning if both Ronaldo and Messi are in the team?
So, using notations -
Given,
P(Win | Messi playing) = 0.8 and
P(Win | Ronaldo playing) = 0.6
What is P(Win | both playing) = ?
Can you give me some directions on how to solve the problem? (Assuming it is solvable)
EDIT
Here is another version of the problem -
Probability of rain is 0.8 if temperature drops more than 5 degree. Probability of rain is 0.6 if pressure drops 10%. What is the probability of rain if temperature drops more than 5 and pressure drops 10%? Assume temperature drop and pressure drops are independent events.