Download Math AE homework #6-10

Homework #6
1. Four chips, numbered 1,2,3, and 4, are in a hat. One chip is drawn and then, without
replacement, a second chip is drawn.
(a) Draw a tree diagram or list the sample space showing all possible outcomes.
(b) What is the probability that one of the two numbers drawn is odd and the other is even?
(c) What is the probability of drawing two prime numbers?
(d) What is the probability that the sum of the two numbers drawn is not less than 5?
(e) What is the probability that the sum of the two numbers is greater than 7?
2. A jar contains one dime, two quarters, and three nickels. Without looking, Andrew picks one
coin from the jar. Without replacing this coin, he picks another coin.
(a) Draw a tree diagram or list the sample space of all possible outcomes.
(b) What is the probability Andrew picked a dime first and then a nickel?
(c) What is the probability he picked two dimes from the jar?
(d) What is the probability he picked two coins such that the sum of their values is greater
than or equal to 35 cents?
3. Spin once. Find P(green)
4. A fair coin is tossed in the air four times. If the coin lands with the head up on the first three
tosses, what is the probability that the coin will land with the head up on the fourth toss?
(a) 0
(b)
1
16
(c)
1
8
(d)
1
2
5. Paloma has 3 jackets, 6 scarves, and 4 hats. Determine the number of different outfits
consisting of a jacket, scarf, and a hat that Paloma can wear.
6. When Kimberly bought her new car, she found that there were 72 different ways her car
could be equipped. Her choices included four choices of engine and three choices of
transmission. If her only other choice was color, how many choices of color did she have?
(a) 6
(b) 12
(c) 60
(d) 65
7. If P( A)  .3, P( B)  .35 and ( A  B)   , then P(A or B) =
(a) .05
(b) .38
(c) .65
(d) 0
8. Roll a die. Find P(ten).
Homework #7
1.
Two blue marbles and three red marbles are in a bag. Without looking, Joan picks a marble from the
bag and notes its color. Without replacing the marble, she chooses a second marble at random and
notes its color. The tree diagram represents all possible outcomes with the probability value on each
branch.
(a) Find the values of x and y
(b) Find the probability that:
(1) two red marbles are selected
(2) at least one blue marble
(3) one blue and one red marble
2.
One black marble and two red marbles are in a bag. Erika picks a marble from the bag at random. She
looks at it, returns it, and makes a second random selection.
(a) Draw a tree diagram or list the sample space showing all possible outcomes
(b) What is the probability that two red marbles were selected?
(c) What is the probability that two black marbles were selected?
(d) What is the probability that one black and one red marble were selected?
(e) What is the probability that at most one black marble was selected?
3.
Spin once. Find P(blue)
4.
If the probability that it will rain on Thursday is
5
, what is the probability that it will not rain on
6
Thursday?
(a) 1
(b) 0
(c)
1
6
(d)
5
6
5.
A certain car comes in three body styles with a choice of two engines, a choice of two transmissions,
and a choice of six colors. What is the minimum number of cars a dealer must stock to have one car of
every possible combination?
(a) 13
(b) 36
(c) 42
(d) 72
6.
In a sophomore class of 340 students, some study Spanish, some study French, some study both
languages, and some study neither language. If P(Spanish) = .7, P(French) = .4, and P(Spanish and
French) = .25, find:
(a) the probability that a sophomore studies Spanish or French
(b) the number of sophomores who study one or more of these languages
7.
Flip a coin. Find P(3).
8. Find P(rolling a 4 and flipping a head)
Homework #8
1. A candy jar has four red gumdrops, five green gumdrops, and one black gumdrop. Without
looking, Kim reaches into the jar and chooses one gumdrop. Without replacing this gumdrop,
Kim chooses a second gumdrop. The tree diagram represents all possible outcomes with the
probability value on each branch.
(a) Find the values of x, y, and z
(b) Find the probability that:
(1) both gumdrops are green
(2) one of the gumdrops is red and the other is green
(3) neither gumdrop is red
2. The party registration of the voters in Jonesville is shown in the table. If one of the registered
Jonesville voters is selected at random, what is the probability that the person selected is not a
Democrat?
(a) 0.333
(b) 0.400
(c) 0.600
(d) 0.667
3. A softball team plays two games each weekend, one on Saturday and the other on Sunday.
The probability of winning on Saturday is
3
4
and the probability of winning on Sunday is .
5
7
What is the probability of:
(a) losing a Saturday game
(b) losing a Saturday game and winning a Sunday game
(c) winning a Sunday game after already winning a Saturday game
(d) winning both games
(e) losing both games
4. In how many different ways can 5 students be arranged in a row?
5. How many different 6-letter arrangements can be formed using the letters in the work
“ABSENT”, if each letter is used only once?
(a) 6
(b) 36
(c) 270
(d) 46656
6. There were seven students running in a race. How many possible different arrangements of
first, second and third place are possible?
7. Find the probability of choosing a black king from a standard card deck?
8. Spin once. Find P(red)
Homework #9
1. A fair die and fair coin are tossed.
(a) List the sample space for all possible outcomes for one roll of the dice and one flip of the
coin.
(b) Find the probability of getting:
(1) an odd number and a head
(2) a number greater than 5 and a tail
(3) a number greater than 4 or a head
(4) a prime number and either a head or a tail
2. Draw a tree diagram for problem #1
3. A fair coin is tossed three times. What is the probability that the coin will land tails up on the
second toss?
(a)
1
3
(b)
1
2
(c)
2
3
(d)
3
4
4. How many different 4 digit numbers can be made using the digits 2,4,6, and 8 if each digit
only appears once in each number?
5. Evaluate:
6. Evaluate:
7
P4
7!
3!
7. How many different 4-letter arrangements can be formed using the letterss of the word
“JUMP” if each letter is used only once?
(a) 24
(b) 16
(c) 12
(d) 4
8. A locker combination system uses three digits from 0 to 9. How many different three-digit
combinations with no digit repeated are possible?
(a) 30
(b) 504
(c) 720
(d) 1000
9. Find P(snow in summer in NYS)
Homework #10
1. Lunch at the school cafeteria consists of a sandwich, a dessert, and a beverage. The sandwich
choices are tuna, ham, or peanut butter. Dessert is a cookie or Jell-O, and the beverage is
either mile or orange juice.
(a) List the sample space for all possible lunches
(b) Find the probability of a student having a tuna sandwich, Jell-O, and milk
(c) Find the probability of a student having milk as the beverage
(d) Find the probability of a student having a ham sandwich, a cookie or Jell-O, and orange
juice
2. Draw a tree diagram for problem #1
3. A box contains six black balls and four white balls. What is the probability of selecting a
black ball at random from the box?
(a)
1
10
(b)
6
10
(c)
4
6
(d)
6
4
4. How many different 4 digit numbers can be made using the digits 2,1,6, and 8 if repetition is
allowed?
5. Evaluate:
5
P2
6. Evaluate: (3  2)!
7. How many different arrangements of 10 letters can be made from the letters in the work
BOOKKEEPER?
8. How many different five-digit numbers can be formed from the digits 1,2,3,4, and 5 if each
digit is used only once?
(a) 120
(b) 60
(c) 24
(d) 20
9. All seven-digit telephone numbers in a town begin with 245. How many telephone numbers
may be assigned in the town is the last four digits do not begin or end in zero?
10. How many committees of 4 students can be formed from a class of 15 students?
11. Evaluate:
5
C2