MathNoob123
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- Oct 5, 2013
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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
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