Math 1342 Review 2
1. A popular brand of pen comes in red, blue, or black ink. The writing tip can be chosen from extra bold, bold, regular, fine, or micro. How many different choices of pens do you have with this brand?
2. Six acts are scheduled to perform in a variety show. How many different ways are there to schedule their appearances?
3. A club with 15 members is to choose four officers – president, vice-president, secretary, and treasurer. In how many different ways can these offices be filled, if no member can hold more than one office?
4. Suppose A and B are two events with and . Find if the two events are
a) mutually exclusive b) independent
5. A carton of 24 light bulbs includes three that are defective. If two of the bulbs are chosen at random without replacement, what are the probabilities that
a) neither bulb will be defective? b) exactly one of the bulbs will be defective?
6. If , , and
a) Complete the following probability diagram.
b) Find c) Find d) Find
e) Find f) Are A and B independent? g) Are A and B mutually exclusive?
Why? Why not? Why? Why not?
7. Diagnostic tests of medical conditions have several results. The test result can be positive or negative and the patient can either have the condition or not. The results of a new diagnostic test for 200 patients are given in the following table:
Condition Present / Condition Absent /Total
Test Result + / 110 / 20 / 130Test Result - / 20 / 50 / 70
Total / 130 / 70 / 200
If a person is selected at random, find the following probabilities:
a) b)
c) d)
8. A political discussion group consists of 4 Republicans and 6 Democrats. If a committee of four people is selected at random, find the probability that
a) all four are Democrats. b) two are Democrats and two are Republicans.
9. A box contains 5 red marbles, 6 green marbles, and 9 yellow marbles. You select one marble at random and do not replace it. Then you randomly select a second marble.
a) Complete the following probability tree:
b) Find the probability that both marbles selected are green.
c) Find the probability that the second marble selected is red.
d) Find the probability that the first marble selected was red given that the second marble selected is yellow.
10. Determine if the following probability distributions are valid. If not, tell why.
a) b)
11. The manager of a retail clothing store has determined the following probability distribution for X, the number of customers who will enter the store on Saturday.
X / 10 / 20 / 30 / 40P(X) / .2 / .2 / .4 / .2
a) Complete the table to find the mean number of customers who will enter the store on Saturday.
10 / .2 / 220 / .2
30 / .4
40 / .2
Total
b) Complete the table to find the variance of the number of customers who will enter the store on Saturday.
10 / .220 / .2 / 36 / 7.2
30 / .4 / 16 / 6.4
40 / .2
Total
c) Find the standard deviation of the number of customers who will enter the store on Saturday.
d) Find the probability that more than 30 customers will enter the store on Saturday.
e) Find the probability that at most 20 customers will enter the store on Saturday.
f) Find the probability that at least 30 customers will enter the store on Saturday.
12. A game is played by randomly selecting one bill from a bag that contains ten $1 bills, five $2 bills, three $5 bills, one $10 bill, and one $100 bill. The player gets to keep the selected bill.
a) Complete the table of amounts of money won and their probabilities:
X / $1 / $2 / $5 / $10 / $100P(X) /
b) If the player must pay $20 to play this game, what is the expected value of the game?
13. If X is binomial with and , then find the following:
a) the mean of X b) the standard deviation of X
c) d) e)