Answer:
Step-by-step explanation:
For first game PA = 1/3
For second game PA = 1/3 ( If A is not lost in first game )
= 2/5 (If A is lost in first game )
For conclusion of game in three matches :
If A wins , the probability is
PA , PB , PA = 1/3 X 2/3 X 3/5 = 6/45
PB , PA , PA = 2/3 X 3/5 X 1/3 = 6/45
If B wins
PA, PB, PB = 1/3 X 2/3 X 2/5 = 4/ 45
PB, PA , PB = 2/3 X 3/5 X 2/3 = 4 / 15
Total probability of conclusion of game in 3 matches
= 6/45 +6/45 + 4/45 +4/15 = 28/45
b )
For the game concluding in 2 matches , the probability are as follows
PA,PA = 1/3 X 1/3 = 1/9
PBPB = 2/3 X 2/5 = 4 / 15
Total probability
= 1/9 + 4/15 = 17/45
So PA = 1/9 / 17/45
= 5/17
