Atournament is being run between two teams, a and b. this is a 2- tournament meaning that the first team to win 2 games is the tournament winner (sometimes called a best-two-out-of-three tournament). for the first game, the probability of a winning is pa wins]-1/3. for all ensuing games the probability that team a wins is pa wins- 1/3 unless team a lost on the previous round in which case pa wins-3/5.

a: what is the probability that the tournament requires the full three games to decide a winner?
b: the tournament concludes after two games. what is the probability that a won?

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

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

step-by-step explanation: