# !!Probability Problems!!?

1) If the odds in favour of Ann beating Sue in a chess game are 5:4, what is the probability that Sue will win an upset victory in a best-of-five chess tournament?

2) Suppose the odds of the Toronto Maple Leafs winning the Stanley Cup are 1:5, while the odds of the Montreal Canadiens winning the Stanley Cup are 2:13. What are the odds in favour of either Tonronto or Montreal winning the Stanley Cup?

3) 4 friends, 2 girls and 2 boys, are playing contract bridge. Partners are randomly assigned for each game. What is the probability that the 2 girls will be partners for the first game?

4) Ann,Sue,Amy,Ken,and Kim are going to a party. What is the probability that 2 of the girls will arrive first?

5) A hockey team has 2 goalies,6 defenders,8 wingers,and 4 centres. If the team ramdomly select 4 players to attend a charity function, what is the likehood that no goalies or centres are selected?

Relevance

q1

what's upset victory?

i'll just make up the rule that upset victory in best of 5 is winning all last 5 from 9 games.

so the winning sequence=AAAASSSSS; the only way it happen

P=(5/9)^4(4/9)^5

=4*20^4/9^9

=640000/387420489

=0.001652

=0.1652%

edit q1

i just feel like changing make-up rules a bit. best of 5 needs you to win 3 to win the game. and this time sue get to win in many ways.

P(sue wins the game)

=P(in 5 sets)+P(in 4 sets)+P(in 3 sets)

=5C3s^3*a^2 + 4C3s^3*a + 3C3s^3

=[10(5/9)^2 + 4(5/9) + 1]*(4/9)^3

=[250+180+81]*64/9^5

=511*64/9^5

=0.553845

=55.3845%

q2

TML=1:5=1/6=5/30

MC=2:13=2/15=4/30

P=1/(1+5) + 2/(2+13)

=1/6+2/15

=(5+4)/30

=9/30

=3/10

odds favouring either one

=3:(10-3)

=3:7

q3

how do you play contract bridge?

P=2*2C2/4C2

=2/6

=1/3

q4

sorry, but i'm not good with names. Kim's a girl or boy? Kim's my surname, so i dont know. we'll assume ken's the only boy here.

P=4*3*3*2*1/5*4*3*2*1

=3/5

q5

likelihood?

2 goalies,6 defenders,8 wingers,and 4 centres

P(no goalies or centers)

=(6+8)C4/(2+6+8+4)C4

=14C4/20C4

=11*12*13*14/17*18*19*20

=11*13*7/17*19*15

=1001/4845

=0.2066

=20.66%