for ST371-002 Smith Section Spring 2011

HW # 2 Due Tuesday Feb 8, 2011

Last 2 problems are in Devore.

1. How many distinguishable ways can the word HUMUHUMUNUKUNUKUAPUAA be arranged.

2.  In a Calif. study, Dean Lester Breslow  and Dr. James  Enstrom of the UCLA School of Public Health  concluded that
by following 7 simple health rules a man's life can be extended by 11 years  on the average, and a women's life by 7 years.

    The 7 rules are:
    1.  no smoking
    2.  regular exercise
    3.  use alcohol moderately
    4.  get 7 to 8 hours of sleep nightly
    5.  maintain proper weight
    6.  eat breakfast
    7.  do not eat between meals
  In how many ways can a person adopt exactly FIVE of these rules  IF :

        a)  the person presently violates all 7 rules??
        b)  the person already never drinks and always eats breakfast ??
HINT: does order matter ?

3.   Suppose that the study in problem 2 had sampled a senior college class made up of 500 students.

they found:
210 students smoked
258 drank alcoholic beverages
216 eat between meals
122 both smoke and drink alcoholic beverages
83   both eat between meals and drink alcoholic beverages
97   both smoke and eat between meals
52   have all 3 bad habits: smoke, drink alcoholic beverages, eat between meals

If a member of this senior class is selected at random ,
 find the probabilty that the student:
    a) smokes but does NOT drink alcoholic beverages
    b) eats between meals AND drinks alcoholic beveraves BUT does NOT smoke
    c) neither smokes nor eats between meals

Hint: draw a Venn diagram
4.   In an article in the News and Disturber  newspaper from a group of exactly 2000 people
they reported that there are exactly:
    612 people who smoke
    670 people who are over 25 years of age
    960 people who imbibe
    86 smokers who imbibe
    290 imbibers who are over 25 years of age
    158 smokers who are over 25 years of age
    44 people over 25 years of age each of whom both smokes and imbibes   
    250 people under 25 years of age who neither smoke nor imbibe

DETERMINE whether or not this report is CONSISTENT, that is do the numbers
in the Venn diagram add up to 2000.
5.  FULLY EXPLAIN your answers to the following questions:
    a)  IF events A and B  are mutually exclusive (disjoint)  AND  collectively exhaustive,
          ARE the events A'  and B'  mutually exclusive ??
IF events A and B  are mutually exclusive (disjoint)  BUT NOT  collectively exhaustive,
ARE the events A'  and B' collectively exhaustive ??
IF events A and B  are  collectively exhaustive BUT NOT  mutually exclusive (disjoint),
ARE the events A'  and B' collectively exhaustive ??
6.    How many ways can 6 boys and 7 girls sit in a row,
 if the boys and girls must alternative seats ?
7.   Five married couples have bought 10 tickets in a row for the upcoming Bon Jovi concert at the RBC in feb.,

In how many different ways can they be seated
        a)  with no restrictions.
        b)    if each couple is to sit together
        c)    if all the men sit to the left of all the women.

8.  In a soon-to-be released, low budget Halloween martial arts movie, a featured pumpkin has the starring role.
Due to the rather violent nature of the film, a STUNT pumpkin has also been hired.

Suppose that the featured pumpkin appears in 40 % of all the film's scences,
the STUNT pumpkin appears in 30 % of all scences,
the two pumpkins appear SIMULTANEOUSLY in 5 % of all scences.

What is the probability that in a given scence,
        a)  ONLY the STUNT pumpkin appears ?

        b)  NEITHER pumpkin appears ?


problem 9. text, p. 65, # 30
problem 10. text, p. 59, # 26