MGSC 1206.2
SOLUTIONS: Assignment #1
Winter 2008
TOTAL MARKS = 75
Due:
1 pm, Friday, January 18
th
7.3 #22. A single fair die is rolled. Find the probability of the event “getting a number greater than 2”.
Let E = “getting a number greater than 2”
S = {1,2,3,4,5,6} so n(S)=6. The numbers greater than 2 are 3, 4, 5, 6 so n(E) = 4.
P(E) = n(E) / n(S) = 4/6 = 0.67
7.3 #24. A single fair die is rolled. Find the probability of the event “getting any number except 3”.
Let E = “getting any number except 3”
S = {1,2,3,4,5,6} so n(S)=6. The numbers other than 3 are 1, 2, 4, 5, 6 so n(E) = 5.
P(E) = n(E) / n(S) = 5/6 = 0.83
7.3 #44. In 1998, funding for university research in the US totaled $26.343 billion. Support came from
various sources, as shown below.
Source
Amount (in billion $)
Federal government
15.558
State and local government
2.070
Industry
1.896
Academic institutions
4.979
Other
1.840
Find the probabilities that funds for a particular project came from each of the following sources:
(a) federal government,
(b) industry,
(c) academic institutions.
We will assume that the probability that a particular project had funds from a given source is
proportional to the fraction of total funds coming from that source.
a.
P( funds came from federal government ) = 15.558 / 26.343 = 0.591
b.
P( funds came from industry ) = 1.896 / 26.343 = 0.072
c.
P( funds came from academic institutions ) = 4.979 / 26.343 = 0.189
Thus the probabilities of funds coming from federal government, industry, or academic
institutions are 59.1%, 7.2% and 18.9% respectively.
1
2 pts
2 pts
3 pts