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## Homework Statement

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.

## Homework Equations

none

## The Attempt at a Solution

a) P(A wins) = 0.345, P(B wins) = 0.436, P(tie) = 0.219

Hi, I found out the probabilities each time wins. I can't figure out the answers to B or C however. Any ideas?

Thanks