Spring 2007
Math 227(March 28, 07)
Name: ______________________
Show all necessary work NEATLY, UNDERSTANDABLY and SYSTEMATICALLY for full points.
Any understatement and/or false statement may be penalized. This is a closed book, closed note
and closed neighborhood test. If you are using a TI calculator, you must write down exactly what
was input to the calculator. Total is 120 points. Good Luck!
1. A box contains five green marbles, eight red marbles, and three white marbles.
(a). Let A be the even that a red marble is drawn if we randomly select one marble out of this
hat.
(2 points) What is the probability of A? _______________
(2 points) What is the complementary event of A?_________________
(2 points) What is the probability of the complementary event of A? ______________
(b). (4 points) If two marbles are drawn without replacement, find the probability that both of them
are red.
5. The following table gives a two-way classification of 1000 couples based on whether one or both
spouses work and whether or not they have children.
Work Status
Have Children
Yes
No
Both Spouses Work
140
260
Only one Spouse Works
380
220
Select one couple randomly from these 1000 couples and find the following probabilities that
(a). (3 points) Both spouses work and have no children.
(b). (3 points) Only one spouse works and have children.
(c). (3 points) Both Spouses work given that they have no children.
(d). (3 points) Only one Spouses work or they have children.
2.
In California’s Super Lotto Plus lottery game, winning the jackpot requires that you select the
correct 5 numbers between 1 and 47 and, in a separate drawing, you must also select the correct
single number between 1 and 27.
(a)
(5 points) Find the total numbers of possible tickets.
(b)
(5 points)
Find the probability of winning the jackpot.
3. In a study of the MicroSoft gender-selection method, couples in a control group are not given a
treatment, and they each have three children. The probability distribution for the number of girls
is given.
X
P(x)
0
0.150
1
0.350
2
0.375
3
0.125
(a). (6 points) Find the mean and standard deviation for the given probability distribution.
(b). (4 points) Using the above probability distribution, find the probability that a randomly selected
family has at most 2 girls.
4.
In a batch of 8,000 clock radios 7% are defective. A sample of 6 clock radios is randomly
selected without replacement from the 8,000 and tested. The entire batch will be rejected if at
least one of those tested is defective. What is the probability that the entire batch will be
rejected?
(8 points)
5. (a). (5 points) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if
repetition of digits is not allowed?
(b). (5 points) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if
repetition of digits is allowed?
6. According to a survey, 56% of Baby Boomers have car loans and are making payments on these
loans. Assume that this result holds true for the current population of all Baby Boomers.
(a). (5 points) Find the probability that in a random sample of 12 Baby Boomers, exactly 10 have
car loans and are making payments on these loans.
(b). (5 points) Find the probability that in a random sample of 12 Baby Boomers, at least 3 have car
loans and are making payments on these loans.
(c).
(4 points)
Find the mean and standard deviation.
7. On average, 25 new accounts are opened per week (5 working day) at a local bank.
(a). (3 points) Find the mean number of new accounts per day.
(b). (3 points) Find the probability that on a given day the number of new account opened at this
bank will be exactly 4
(c). (4 points) Find the probability that on a given day the number of new account opened at this
bank will be at least 3
8. An instant raffle ticket costs $2.00. Out of 10,000 tickets for this raffle, 1000 tickets contain a
prize of $5.00 each, 100 tickets have a price of $10 each, 5 tickets have a prize of $1000 each,
and 1 ticket have a prize of $5000. Let x be the random variable that denotes the net amount of a
player wins by playing.
(a). (6 points) Construct the probability distribution of x.
(b). (4 points) Find the expected value.
9. In a club with 7 men and 12 women members
(a). (3 points) How many 5-member committees can be chosen that have 3 men and 2 women?
(b).
(3 points)
How many 5-member committees can be chosen that have no more than 3 women?
(c). (4 points) If this club must elect a president, a vice president, and a secretary, how many
different slates of candidate are possible?
(d). (5 points) Find the probability of selecting a 5-member committee that consists of all men?
10. For a standard normal distribution. Find the indicated probability. For each case, draw a sketch.
(a). (3 points) P( z  0.52)
(b).
(4 points)
P( 115
.  z  2.34)
(c).
(4 points)
P( z  131
. )