### Probability Presentation 4:Review

```Probability
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.
(a) 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
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
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
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.
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 30 2005 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
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)=1-0.425
0.575
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
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
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)
1-0.3306
0.670
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
1000-1999
84,791
11,010
974
96,775
2000-2999
252,116
661,510
37,657
951,283
3000-3999
145,506
2,375,346
172,957
2,693,809
4000-4999
8,747
292,466
27,620
328,833
Over 5000
192
3,994
483
4,669
Total
521,116
3,344,549
239,706
4,105,371
Question 3
(a) What is the probability that a randomly selected baby born in 2005 was
postterm?
Question 3
(b) What is the probability that a randomly selected baby born in weighed
between 3,000 and 3,999 grams?
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?
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?
Question 3
(e) What is the probability that a randomly selected baby born in 2005 weighed
less than 1,000 grams and was postterm?
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?
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
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:
C
29 5
Qtn: The fixed-price dinner at a restaurant provides the following choices:
Entrée: baked chicken, broiled beef patty, baby beef liver, roast beef
Desert: ice cream or cheese cake