1. Probability

2. Question 1
In the game of roulette, a wheel consists of 38 slots, numbered 0,00,1, 2,…,36. To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0, 00 are green, the odd numbers are red, and the even numbers are black.
Determine the probability that the metal ball falls into a green slot
Solution:
G= The event of a metal ball falling in a green slot
Sample space= 0,00,1,2,…,36
Number in sample space=38
P(G)=N(G)/N(S)
P(G)=2/38=1/19

3. Question 1
In the game of roulette, a wheel consists of 38 slots, numbered 0,00,1, 2,…,36. To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0, 00 are green, the odd numbers are red, and the even numbers are black.
(b) Determine the probability that the metal ball falls into a green or red slot
Solution:
R= The event of a metal ball falling in a green or red slot
Sample space= 0,00,1,2,…,36
Number in sample space=38
P(R)=N(R)/N(S) + N(G)/N(S)
P(R)=18/38 + 2/38 = 10/19

4. Question 1
In the game of roulette, a wheel consists of 38 slots, numbered 0,00,1, 2,…,36. To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0, 00 are green, the odd numbers are red, and the even numbers are black.
(c) Determine the probability that the metal ball falls into 00 or a red slot
Solution:
B= The event of a metal ball falling in a 00 or red slot
Sample space= 0,00,1,2,…,36
Number in sample space=38
P(B)=1/38 +18/38 = 19/38

5. Question 1
In the game of roulette, a wheel consists of 38 slots, numbered 0,00,1, 2,…,36. To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0, 00 are green, the odd numbers are red, and the even numbers are black.
(d) Determine the probability that the metal ball falls into the number 31 and a black slot simultaneously. What term can be used to describe this event?
Solution:
E= The event of a metal ball falling into the number 31 and a black slot simultaneously.
Sample space= 0,00,1,2,…,36
Number in sample space=38
P(E) = 0
The number 31 is odd hence its slot is colored red. There is no way a metal ball can fall into a red slot and a black slot at the same time.
This event is described as impossible.

6. Question 2
Between 6:00pm December 30,2005, and 5:59am January 3, 2006, there were 454 traffic fatalities in the United States. Of these 193 were alcohol related.
(a) What is the probability that a randomly selected traffic fatality that happened between 6:00pm December and 5:59 am January 3,2006 was alcohol related?
Solution:
A= The event of a traffic fatality being alcohol related
P(A)=N(A)/N(S)
P(A)=193/454
0.425

7. Question 2
Between 6:00pm December 30,2005, and 5:59am January 3, 2006, there were 454 traffic fatalities in the United States. Of these 193 were alcohol related.
(b) What is the probability that a randomly selected traffic fatality that happened between 6:00pm December 30,2005 and 5:59am January 3,2006 was not alcohol related?
Solution:
A= The event of a traffic fatality being alcohol related
N= The event of a traffic fatality not being alcohol related
P(A)+P(N)=1
P(N)=1-P(A)
P(N)=
0.575

8. Question 2
Between 6:00pm December 30,2005, and 5:59am January 3, 2006, there were 454 traffic fatalities in the United States. Of these 193 were alcohol related.
(c) What is the probability that two randomly selected traffic fatalities that happened between 6:00pm December 30,2005 and 5:59am January 3,2006 were both alcohol related
Solution:
C= The event of two traffic fatalities being alcohol related
P(C)= 193/454 *193/454
0.181

9. Question 2
Between 6:00pm December 30,2005, and 5:59am January 3, 2006, there were 454 traffic fatalities in the United States. Of these 193 were alcohol related.
(d) What is the probability that neither of two randomly selected traffic fatalities that happened between 6:00pm December 30,2005 and 5:59am January 3,2006 were both alcohol related
Solution:
N= The event of neither two traffic fatalities being alcohol related
P(N)= 261/454 *261/454
0.3306=0.331

10. Question 2
Between 6:00pm December 30,2005, and 5:59am January 3, 2006, there were 454 traffic fatalities in the United States. Of these 193 were alcohol related.
(e) What is the probability that of two randomly selected traffic fatalities that happened between 6:00pm December 30,2005 and 5:59am January 3,2006, at least 1 was alcohol related
Solution:
E= The event of at least 1 of two randomly selected traffic fatality being alcohol related
N= The event of neither two randomly selected traffic fatality being alcohol related
P(E)+P(N)=1
P(E)=1-P(N)
0.670

11. Question 3
The following data represent the birth weights (in grams) of babies born in 2005, along with the period of gestation.
Birth Weight (grams)
Pre-term
Term
Post-term
Total
Less than 1000
29,764
223 15
30,002
84,791
11,010
974
96,775
252,116
661,510
37,657
951,283
145,506
2,375,346
172,957
2,693,809
8,747
292,466
27,620
328,833
Over 5000
192
3,994
483
4,669
521,116
3,344,549
239,706
4,105,371

12. Question 3
(a) What is the probability that a randomly selected baby born in 2005 was postterm?

13. Question 3
(b) What is the probability that a randomly selected baby born in weighed between 3,000 and 3,999 grams?

14. Question 3
(c) What is the probability that a randomly selected baby born in weighed between 3,000 and 3,999 grams and was postterm?

15. Question 3
(d) What is the probability that a randomly selected baby born in weighed between 3,000 and 3,999 grams or was postterm?

16. Question 3
(e) What is the probability that a randomly selected baby born in 2005 weighed less than 1,000 grams and was postterm?

17. Question 3
(f) What is the probability that a randomly selected baby born in 2005 weighed between 3000 to 3999, given the baby was postterm?

18. Question 4
In a game of Jumble, the letters of the word are scrambled. The player must form the correct word. In a recent game in a local newspaper, the jumble word was LINCEY. How many different arrangements are there of the letters in this word?
Solution:
There are six possible ways to arrange the word LINCEY.
6! = 720

19. Question 5
The US Senate Appropriations Committee has 29 members and a subcommittee is to be formed by randomly selecting 5 of its members. How many different committees could be formed?
Solution:

20. Qtn: The fixed-price dinner at a restaurant provides the following choices:
Appetizer: soup or salad
Entrée: baked chicken, broiled beef patty, baby beef liver, roast beef
Desert: ice cream or cheese cake

21. CSTEM Web link http://www.cis.famu.edu/~cdellor/math/
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