MATH 367, spg 98, CHAPTER 1

1. A, B and C are to work on the computer All. They will draw lots to determine the order in which they will use the machine.

(a) List all the elements of a suitable sample space, if all orders need to be distinguished.

(b) Mark with a check the elements of the event “A uses the computer before C does”.

(c) Mark with a cross the elements of the event “C uses the com-

puter between A and B”.

2. A coin is tossed repeatedly until it falls the same twice in a row. (a) Describe the sample space.

(b) Describe the events “the coin is tossed exactly 5 times”.

3. A coin is tossed repeatedly until the first head appears. (a) Describe the sample space.

(b) Decribe the event “the coin is tossed exactly 5 times”.

(c) Describe the event “the coin is tossed at least 5 times”.

(d) Describe the event “the coin is tossed at most 5 times”.

4. A certain town of population 100,000 has 3 newspapers: I, II, III. The proportion of town people that read these papers are as follows:

I: 10 % I and II: 8 % I and II and III: 1 % II: 30 % I and III: 2 % III: 5 % II and III: 4 %

(a) Find the number of people reading only one newspaper.

(b) How many people read at least two newspapers?

(c) If I and III are morning papers and II is an evening paper, how many people read at least one morning paper plus an evening paper?

(d) How many people read only one morning paper and one evening

paper?

5. Urn A contains 3 red and 3 black balls. Urn B contains 4 red and 6 black balls. A ball is randomly selected from each urn.

(a) Describe the sample space.

(b) What is the probability that the ball from urn A is red?

(c) What is the probability that the ball from urn B is red?

(d) What is the probability that the two balls are of the same

color?

6. Show that for any events A, B and C:

P (A ∩ B) + P ((A\B) ∪ (B\A)) + P (Ā ∩ B̄) = 1

For next class, Fri Jan 23: read chapter 1 and do problems 2, 3, 4, 5, 6, 7.