prettylittlepixels
New member
- Joined
- Nov 15, 2013
- Messages
- 32
It is election day on McCoy Isle. 8% of the residents live in rural areas (R), 13% live in Littleville (L), 27% live in Middletown (M), and 52% live in Hugecity (H). There are three candidates running for the office of Overlord: Spendthrift Sue (S), Balanced-Budget Bob (B), and Environmental Ed (E).
Of the rural residents (GIVEN RURAL), 20% favor Sue, 15% favor Bob, and 65% favor Ed.
Of the Littleville residents, 20% favor Sue, 25% favor Bob, and 55% favor Ed.
Of the Middletown residents, 30% favor Sue, 25% favor Bob, and 45% favor Ed.
Of the Hugecity residents, 40% favor Sue, 45% favor Bob, and 15% favor Ed.
You can answer these questions using just the probability formulas, but most students will find a contingency table or a tree diagram helps to organize your thoughts.
I made the following contingency table
If every resident votes and the candidate with the most votes becomes Overlord, who will be the new Overlord?
-Sue
-There will be a tie.
-Ed
-Bob
Bob because .346 is the largest probability on my contingency table:
(.08*.15)+ (.13*.25)+ (.27*.25)+ (.52*.45)= 0.346
Sue’s came out to .331 and Ed’s came out to .323
If an individual is chosen at random, what is the probability that the person is a Littleville resident and favors Bob?
.13*.25= 0.0325
If a resident is chosen at random, what is the probability that the person is either a resident of Hugecity or favors Sue or both?
I’m pretty sure I didn’t do this problem right. I think the word or in the problem is throwing me off because I calculated:
P(H and S)= .52 * .331= 0.17212
P(H or S)= P(H) + P(S) – P(H and S)= .52 + .331 - .17212= .67888
So I then added .67888+ .17212= 0.851 but this doesn’t sound right. The question says is either a resident of Hugecity or favors Sue or both. The 2 or’s in this problem confuse me. Does it mean I should add P(H) + P(S) + P(H and S)= .52+.331+.17212= 1.02312, but this can’t be right because the probability can’t be more than 1…
A randomly-chosen resident favors Ed. What is the probability that the person is a rural resident?
For this problem I took P(E) * P(R)= .323 * .08= .02584 or should I do .08/.323= .2477?
A randomly-chosen resident favors Bob. What is the probability that the person is a resident of Middletown?
Same as the part of the question above. P(B) * P(M)= .346*.27= .09342 or is this not right?
A randomly-chosen citizen favors Sue. What is the probability that the citizen is NOT a resident of Littleville?
For this problem I:
1-.13= .87
.87*.331= .28797?
Of the rural residents (GIVEN RURAL), 20% favor Sue, 15% favor Bob, and 65% favor Ed.
Of the Littleville residents, 20% favor Sue, 25% favor Bob, and 55% favor Ed.
Of the Middletown residents, 30% favor Sue, 25% favor Bob, and 45% favor Ed.
Of the Hugecity residents, 40% favor Sue, 45% favor Bob, and 15% favor Ed.
You can answer these questions using just the probability formulas, but most students will find a contingency table or a tree diagram helps to organize your thoughts.
I made the following contingency table
| Sue (S) | Bob (B) | Ed (E) |
Rural (R) .08 | .2 | .15 | .65 |
Littleville (L) .13 | .2 | .25 | .55 |
Middletown (M) .27 | .3 | .25 | .45 |
Hugecity (H) .52 | .4 | .45 | .15 |
Total Probabilities | .331 | .346 | .323 |
If every resident votes and the candidate with the most votes becomes Overlord, who will be the new Overlord?
-Sue
-There will be a tie.
-Ed
-Bob
Bob because .346 is the largest probability on my contingency table:
(.08*.15)+ (.13*.25)+ (.27*.25)+ (.52*.45)= 0.346
Sue’s came out to .331 and Ed’s came out to .323
If an individual is chosen at random, what is the probability that the person is a Littleville resident and favors Bob?
.13*.25= 0.0325
If a resident is chosen at random, what is the probability that the person is either a resident of Hugecity or favors Sue or both?
I’m pretty sure I didn’t do this problem right. I think the word or in the problem is throwing me off because I calculated:
P(H and S)= .52 * .331= 0.17212
P(H or S)= P(H) + P(S) – P(H and S)= .52 + .331 - .17212= .67888
So I then added .67888+ .17212= 0.851 but this doesn’t sound right. The question says is either a resident of Hugecity or favors Sue or both. The 2 or’s in this problem confuse me. Does it mean I should add P(H) + P(S) + P(H and S)= .52+.331+.17212= 1.02312, but this can’t be right because the probability can’t be more than 1…
A randomly-chosen resident favors Ed. What is the probability that the person is a rural resident?
For this problem I took P(E) * P(R)= .323 * .08= .02584 or should I do .08/.323= .2477?
A randomly-chosen resident favors Bob. What is the probability that the person is a resident of Middletown?
Same as the part of the question above. P(B) * P(M)= .346*.27= .09342 or is this not right?
A randomly-chosen citizen favors Sue. What is the probability that the citizen is NOT a resident of Littleville?
For this problem I:
1-.13= .87
.87*.331= .28797?