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,
and 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 |
(7)
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
and 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)
