Probability question-- need help

MathNoob123

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A and B are college football teams that have gone into overtime.

In the first round A will go first with the following possible outcomes: no score; 3 points; 6 points; 7 points; 8 points; a turnover where B wins (note in this case the game ends immediately). The probabilities of these happening are: .2, .3, .1, .3, .09, .01.

B then follows with the following conditional outcomes:
if A scored 0–B ties with probability .1; B wins with probability .88; A wins with probability .02.
if A scored 3–B ties with probability .3; B wins with probability .6; A wins with probability .1.
if A scored 6–B ties with probability .01; B wins with probability .4; A wins with probability .59.
if A scored 7–B ties with probability .3; B wins with probability .1; A wins with probability .6.
if A scored 8–B ties with probability .2; A wins with probability .8
If the teams are tied after the first round, they go to a second round and continue until a team wins.

a) Find the probability that: A wins in the first round; B wins in the first round; they’re tied after the first round.
b) Find the probability that A wins.
c) Find the expected number of rounds.

I figured out part a) 0.345, 0.436, and 0.219. Not sure how to do parts b and c. Help! thanks :)
 
A and B are college football teams that have gone into overtime.

In the first round A will go first with the following possible outcomes: no score; 3 points; 6 points; 7 points; 8 points; a turnover where B wins (note in this case the game ends immediately). The probabilities of these happening are: .2, .3, .1, .3, .09, .01.

B then follows with the following conditional outcomes:
if A scored 0–B ties with probability .1; B wins with probability .88; A wins with probability .02.
if A scored 3–B ties with probability .3; B wins with probability .6; A wins with probability .1.
if A scored 6–B ties with probability .01; B wins with probability .4; A wins with probability .59.
if A scored 7–B ties with probability .3; B wins with probability .1; A wins with probability .6.
0.21f A scored 8–B ties with probability .2; A wins with probability .8
If the teams are tied after the first round, they go to a second round and continue until a team wins.

a) Find the probability that: A wins in the first round; B wins in the first round; they’re tied after the first round.
b) Find the probability that A wins.
c) Find the expected number of rounds.

I figured out part a) 0.345, 0.436, and 0.219. Not sure how to do parts b and c. Help! thanks :)
Hint for parts b) and c) is to consider ties. They keep playing till there is no tie.

b) In the final round, the ratio of A to B is always 0.345:0.436, so P(A) = . . .

c) probability of tie = p = 0.219
....probability of not tie = q = 0.781
X = 1 + number of ties
P(X=1) = . . .
P(X=n) = . . .
What does this distribution look like?
 
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