A 15-member Board of Directors
A 15-member Board of Directors is organizing for the upcomingyear.
2. They mustelect a president, a vice-president, and atreasurer. How many different slates of candidates arepossible?
3. They mustchoose four members to serve on the finance committee. How manydifferent committees could be formed?
The age and gender breakdown of the Board is
|
Female |
Male |
|
|
25 – 35 years old |
3 |
2 |
|
36 – 45 years old |
1 |
4 |
|
Over 46 years old |
2 |
3 |
If one member is randomly chosen to organize the annual meeting,what is the probability that the person will be
4. Female
5. A femaleor a person 25-35 years old
6. A malebetween 36 and 45 years old.
The Board has narrowed the options for the annual meeting to thefollowing:
City: Annapolis or Baltimore
Month: March or June or September
Venue: Hotel or College
7. Draw atree diagram to show the sample space for all possiblechoices.
8. If onepackage is chosen at random what is the probability that it is inAnnapolis at a hotel?
Answer:
Please note nCx = n! / [(n-x)!*x!]
Some important probabilities for faster calculations:
(a) nC0 = 1, eg5C0 =1, 99C0 = 1
(b) nCn = 1, eg10C10= 1, 75C75 = 1
(c) nC1 = n, ,eg5C1= 5, 99C1 = 99
_____________________________________________________
2) Since the president, VP and treasurer cannot hold 2 posts atthe same time, the total possible ways
= 15C1 * 14C1 *13C1
= 15 * 14 * 13 = 2730
______________________________________________________
3) 4 Members for the finance committee. Choose 4 out of 15 =15C4= 1365
______________________________________________________
For Questions 4, 5 and 6
Probability = Favorable Outcomes / Total Outcomes
| Female | Male | Total | |
| 25 – 35years old | 3 | 2 | 5 |
| 36 – 45years old | 1 | 4 | 5 |
| Over 46years old | 2 | 3 | 5 |
| Total | 6 | 9 | 15 |
4) P(That a Randomly chosen person is a Female) = 6/15 =2/5 =0.4
5) P(A Female or a Person 25 – 35 Years Old) = P(Female) + P(Aperson 25 – 35 years old) – P(A Female and a Person 25 – 35 YearsOld)
= 6/15 + 5/15 – 3/15 = 8/15 =0.533
6) (A Male between 36 – 45 years old) = 4/15 = 0.267
__________________________________________________________________________
8) P(Annapolis at a Hotel): By referring to the diagram, therequired probability = 1/4
_________________________________________________________________________
7) The Tree Diagram is as below. The Individual Probabilitiesare
P(Annapolis) = P(Baltimore) = 1/2
P(March) = P(June) = P(September) = 1/3
P(Hotel) = P(College) = 1/2
"Our Prices Start at $11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
