Question

Two teams, the Exponents and the Radicals, square off in a best of 5 math hockey tournament. Once a team wins 3 games, the tournament is over.

The schedule of the tournament (for home games) goes: E-R-E-R-E

If the Exponents are playing at home, there is a 60% chance they'll win. If they are playing on the road, there is a 45% chance they'll win.

Find the probability that the Exponents win the series. Round answers to at least 4 decimal places.

Answer 1

Schedule of the tournament : E-R-E-R-E

E_i : Event of Exponents winning ith game

R_j : Event of Radicals winning jth game

P(E1) = P(E3) = P(E5) = 0.60 -Home games

P(R1)=P(R3)=P(R5) = 1-0.60 =0.40

P(E2)=P(E4) = 0.45 - on the road

P(R2) = P(R4) = 1-0.45 = 0.55

Possibilities -E winning along with probabilities.

1.E1-E2-E3 - P(E1E2E3) = P(E1)P(E2)P(E3) = 0.6*0.45*0.6 =0.162

2.E1-E2-R3-E4 - P(E1)P(E2)P(R3)P(E4) =0.6*0.45*0.40*0.45=0.0486

3.E1-E2-R3-R4-E5 - P(E1)P(E2)P(R3)P(R4)P(E5) = 0.6*0.45*0.40*0.55*0.60=0.03564

4.E1-R2-E3-E4 - P(E1)P(R2)P(E3)P(E4) = 0.6*0.55*0.60*0.40 = 0.0792

5.E1-R2-R3-E4-E5 - P(E1)P(R2)P(R3)P(E4)P(E5) = 0.60*0.55*0.45*0.40*0.60=0.03564

6.R1-E2-E3-E4 - P(R1)P(E2)P(E3)P(E4) = 0.40*0.45*0.60*0.45=0.0486

7.R1-R2-E3-E4-E5 - P(R1)P(R2)P(E3)P(E4)P(E5) =0.40*0.55*0.60*0.45*0.60=0.03564

8.R1-E2-R3-E4-E5 - P(R1)P(E2)P(R3)P(E4)P(E5) = 0.40*0.45*0.40*0.45*0.60=0.01944

9.R1-E2-E3-R4-E5 - P(R1)P(E2)P(E3)P(R4)P(E5) = 0.40*0.45*0.60*0.55*0.60=0.03564

10.R1-R2-E3-E4-E5 - P(R1)P(R2)P(E3)P(E4)P(E5) = 0.40*0.55*0.60*0.45*0.60 = 0.03564

Adding up all the above probabilities will give the probability of Exponents winning = 0.53604