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dddanny2006
- Master | Next Rank: 500 Posts
- Posts: 209
- Joined: Thu Jan 12, 2012 12:59 pm
If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of
2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?
A)24/91
B)45/91
C)2/3
D)67/91
E)84/91
This is how I solve it
Possible combinations =15*14*13*12*11*10*9*8*7*6*5*4 =455
12!
To get atleast 2/3 males in the panel there are 3possibilities
1)8M and 4F
2)9M and 3F
3)10M and 2F
For the first case let the 8 males be already chosen.We only need to find the number of ways in which the females can be chosen. Since we got to select 4 females out of 5 we have 5*4*3*2=5
4!
For the second case let the 9 males be already chosen.We only need to find the number of ways in which the 3 females can be chosen. Since we got to select 3 females out of 5 we have 5*4*3 =10
3!
For the third case let the 10 males be already chosen.We only need to find the number of ways in which the females can be chosen. Since we got to select 2 females out of 5 we have 5*4 =10
2!
Thus 10+10+5=25
Favourable combinations=25/455
Possible combinations
Why am I wrong?
Look at the following problem
An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates
for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4
consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?
a.25
b.35
c.150
d.210
e.300
First, recognize that you need to solve for project manager (PM), team leader (TL), and consultants (C) separately:
PM: one slot, two people = 2
TL: one slot, three people = 3
C: four slots, seven people = 7 * 6 * 5 * 4. With the slot method, you need to then stop and realize that there are 4! ways to rearrange the four people you have chosen. So you need to divide 840 by 24 to get 35 unique teams that can be created. Finally, since 2 of the consultants can't work together, we need to remove these specific teams from the 35 possibilities. If these two people are selected, we have two slots remaining with five other people to fill those slots, so there are 5 * 4 = 20, different ways to select the two other people, divided by 2, because there are 2! ways to choose those two other people. This means there are 35 - 10 = 25 consultant teams that can be selected.
Overall: 2 * 3 * 25 = 150
2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?
A)24/91
B)45/91
C)2/3
D)67/91
E)84/91
This is how I solve it
Possible combinations =15*14*13*12*11*10*9*8*7*6*5*4 =455
12!
To get atleast 2/3 males in the panel there are 3possibilities
1)8M and 4F
2)9M and 3F
3)10M and 2F
For the first case let the 8 males be already chosen.We only need to find the number of ways in which the females can be chosen. Since we got to select 4 females out of 5 we have 5*4*3*2=5
4!
For the second case let the 9 males be already chosen.We only need to find the number of ways in which the 3 females can be chosen. Since we got to select 3 females out of 5 we have 5*4*3 =10
3!
For the third case let the 10 males be already chosen.We only need to find the number of ways in which the females can be chosen. Since we got to select 2 females out of 5 we have 5*4 =10
2!
Thus 10+10+5=25
Favourable combinations=25/455
Possible combinations
Why am I wrong?
Look at the following problem
An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates
for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4
consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?
a.25
b.35
c.150
d.210
e.300
First, recognize that you need to solve for project manager (PM), team leader (TL), and consultants (C) separately:
PM: one slot, two people = 2
TL: one slot, three people = 3
C: four slots, seven people = 7 * 6 * 5 * 4. With the slot method, you need to then stop and realize that there are 4! ways to rearrange the four people you have chosen. So you need to divide 840 by 24 to get 35 unique teams that can be created. Finally, since 2 of the consultants can't work together, we need to remove these specific teams from the 35 possibilities. If these two people are selected, we have two slots remaining with five other people to fill those slots, so there are 5 * 4 = 20, different ways to select the two other people, divided by 2, because there are 2! ways to choose those two other people. This means there are 35 - 10 = 25 consultant teams that can be selected.
Overall: 2 * 3 * 25 = 150
