A) Persons A, B and C plan to have a game night. They arrive independently of each other such that the probability of A arriving is 0.4, B 0.5 and C 0.3. Answers to three decimal places

- What is the probability that the game night will be successful = at least two people will show up?

-There are lights in the room, so at least someone has come. What is the probability that B is there?

-The fourth person D says he will come with a probability of 0.6 if everyone else comes too. Otherwise, D will come with a probability of 0.3. What is the proba- when will D show up?

B) 4 players A,B,C and D play a chess tournament. The pairs of games are drawn and the winners of these games then play to win the tournament. There will be no ties in the games. Based on previous tournaments, the winning probabilities for all mutual games according to the following table have been calculated. For example, A wins With a probability of D of 0.3.

What is the probability that player B will win the tournament? Give the answer to 3 decimal places.

 

A wins A - B 0.6 C 0.4 0.9 B wins 0.4 C wins D wins 0.6 0.7 - 0.1 0.3 0.4 D 0.3 0.7 0.6 -