WRITE CLEARLY AND NEATLY! (numbers in brackets are mark values)

1/ A student can play 0, 1, or 2 hours of raquetball on any given night.
Construct a tree diagram to determine the number of ways that in 3 nights
he can play for a total of 4 hours. (3)

2/ Give the number of ways a student can mark her answers
to a multiple choice test if there are:
a) 8 questions with 3 choices each. (1)
b) 3 questions with 8 choices each. (1)
c) 10 questions with 4 choices each for the first 3 questions,
and 5 choices each for the remaining 7 questions. (2)

3/ There are 6 baseball teams in the American League's eastern division.
In how many ways can:
a) 3 teams finish in 1st, 2nd and 3rd place?
b) all 6 teams finish 1st through 6th? (2)

4/ 2 cards are drawn from a well-shuffled deck of 52 playing cards.
What are the probabilities of getting:
a) 2 jacks? b) 2 clubs? c) an ace and a king? (6)

5/ A student is planning the music she will play at a party. She has 15 tapes
from which she wants to select 6 to play.
In how many ways can she select the tapes if she believes that:
a) the order matters?
b) the order doesn't matter? (4)

6/ A group of investors wants to hire a team of 4 accountants and 2 financial planners.
If they are considering 8 accountants and 5 financial planners for the team:
a) How many 6-person teams can be hired under the given conditions? (2)
b) How many 6-person teams can be hired if no attention is paid to profession? (1)

7/ In the diagram, G is the event that Harry graduates from college this year,
C is the event that Harry's father buys him a car this year.
Explain in words what events are represented by the regions numbered:
a) 1 b) 2 c) 3 d) 4 e) 3 & 4 f) 2 & 3 g) 1 & 2 & 3


8/ A company has discovered a way of evaluating the success of both their
radio and TV advertising. If R is the event that their radio advertising is successful
and T is the event that their television advertising is successful
P(R) = 0.62, P(T) = 0.75, and P(R 3 T) = 0.43, find:
a) P(R') b) P(R 4 T) c) P(R 3 T ') d) P(R 4 T ') (4)

9/ A school has tabulated the favorite snacks of 1000 students in the 2 categories males and females. Here are the results.
(I = ice cream, Z = pizza).

  ice cream pizza total
(M) males 500 125 625
(F) females 200 175 375
total 700 300 1000

If one of these terms is selected at random, find each of the following probabilities:
a) P(M) b) P(I') c) P(M'/Z) d) P(F/I) e) P(Z/M') f) P(F'/Z') (6)

10/ A company estimates that the probability of a recession in the next year is P(R)= 0.4.
They also estimate that the probability that another company distributes a
competing product in the next year is
P(C) = 0.5 . They feel that the probability of
both a recession and a competing product in the next year is
P(R 3 C) = 0.25.
a) If there is a recession, what is the probaility that a company will distribute
a competing product in the next year? (2)
b) If a company produces a competing product, find the probability that there
will be a recession in the next year. (2)
c) Find the probability that there will be either a recession or a competing
product produced or both in the next year. (2)
d) With the appropriate formula, decide whether events R and C are independent (2)

11/ A set of data yield the following: n = 12, Sx = 192, and Sx2 = 3,248.
Find µ the mean,
r2 the variance and r the standard deviation. (3)

TOTAL (50)


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