SOLUTION: can someone please help..thanks Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. Let's suppose tha

Question 190261: can someone please help..thanks
Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. Let's suppose that for each game they play, the probability that the Bears win is 0.54 and the probability the Wildcats win is 0.46.
What is the probability that the bears win the series in 3 games ? .1574
What is the probability that the wildcats win the series in 3 games? .0973
What is the probability that the bears win the series in 4 games? .216
What is the probability that the wildcats win the series in 4 games? .156
what is the probability that the bears win the series in 5 games?
what is the probability that the wildcats win the series in 5 games?
What is the probability that the bears win the series?
what is the probability that the wildcats win the series ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. Let's suppose that for each game they play, the probability that the Bears win is 0.54 and the probability the Wildcats win is 0.46.
What is the probability that the bears win the series in 3 games ? .1575
What is the probability that the wildcats win the series in 3 games? .0973
What is the probability that the bears win the series in 4 games? .216
Patterns are LWWW, WLWW, WWLW
Each has probability (0.54^3)(0.46)= 0.07243
But all three are mutually exclusive so the probability = 3(0.07243)
= 0.2173
----------------------------
What is the probability that the wildcats win the series in 4 games? .156
Prob = 3*0.46^3*0.54 = 0.1577
---------------------------------------------
what is the probability that the bears win the series in 5 games?
# of patterns: 5C2 - 1= 10-1 = 9
Probability of each pattern = (0.54)^3(0.46)^2 = 0.03332
Ans: 9*0.3332 = 0.2999
---------------------------------------------
what is the probability that the wildcats win the series in 5 games?
Ans: 9*(0.46)^3(0.54)^2 = 0.2747
-----------------------------------------------
What is the probability that the bears win the series?
They could win it in 4, or 5, or 6, or 7 games.
Figure each probability and add them.
------------------------------------------
what is the probability that the wildcats win the series ?
Same process as with the bears winning.
===========================================================
Cheers,
Stan H.

RELATED QUESTIONS
In October 2004 the Boston Red Sox won the American League Championship playoff series 4... (answered by stanbon)

There are 10 first-tier national rugby union teams. (a) How many different two-team... (answered by scott8148)

Conditional Probability. (Tree diagram ?) I really don't understand where i have to... (answered by edjones)

solve the following problem using a sytem of two eqaution iin two variables. Hockey teams (answered by ankor@dixie-net.com)

Animal population densities are important to those who manage wildlife. This is... (answered by ikleyn)

Hi. I often want to calculate stuff like the example listed below, but am not sure how (answered by stanbon)

can you please help me solve this problem?! In a large city league, the boys'... (answered by jim_thompson5910)

There are 15 teams in the Eastern Conference of the National Hockey League for 2006-2007... (answered by edjones)

the prairie land base ball conference has 6 teams the teams name are listed below.... (answered by stanbon)