Permutations and Combinations
Theoretical and Experimental
Independent and Dependent Events
Compound Events
WILD!
100
From group of 12 runners, how many ways can you award 1st through 4th place?
11,880 ways
100
The following are the results of tossing number cube 75 times: 1 2 3 4 5 6 10 12 16 15 9 13 What is the experimental probability of rolling a 4?
P(roll a 4)= 15/75 = 1/5 = .2
100
Explain why the event is INDEPENDENT or DEPENDENT. Selecting a red pen, and then a blue pen when choosing 2 pens from a bag of 10 red pens and 15 blue pens with replacement.
Since the first pen is replaced, it is not going to change the probability of selecting the second pen.
100
A bag contains 25 marbles: 10 black, 13 red, and 2 blue. A marble is drawn from the bag at random. Explain why the events "getting a black marble" and "getting a blue marble" are mutually exclusive?
Since you are drawing only a single marble, it is impossible for the marble to be both black and blue at the same time.
100
There are 8 players on the chess team. In how many ways can you select 2 players to start a game?
28 ways.
200
From a group of 10 volunteers, a surveyor chooses 5 to complete a task. How many groups of 5 people can be chosen?
252
200
A paper clip holder has 100 paper clips: 30 are red, 20 are yellow, 25 are green, and 15 are pink. What is the probability the paper clip is NOT PINK?
P(not Pink) = 17/20
200
Explain why the event is INDEPENDENT or DEPENDENT. Each letter of the alphabet is written on a card. Three vowels are drawn without replacement.
The probability of drawing a vowel is 5/26. However, for the second vowel the probability has changed and is now 4/25. The third vowel would have a probability of 3/24. Since the previous event changes the probability. The events are DEPENDENT.
200
With the 10 black marbles, 13 red marbles, and 2 blue marbles. What is the P(red or blue)?
P(red or blue) = 13/25 + 2/25 - 0/25 = 15/25 The intersection of the events is 0!
200
For a number cube, what is the probability of rolling a 2 or a number greater than 4? Is the event mutually exclusive or inclusive? Explain.
P( 2 or >4) = 1/6 + 2/6 = 3/6
300
In one day, a salesman plans to visit 6 out 14 companies in the neighborhood. In how many different orders can visit the companies?
2162160 ways
300
A number cube is rolled twice. What is the probability of getting a 6 at least once? a. 1/36 b. 1/6 c. 11/36 d. 1/3 e. 5/6
c. 11/36
300
There are 2 lemons and 1 lime in a grocery bag. As you pick out the fruit, what is the probability of picking the two lemons first?
P(2 Lemons) = 2/3 * 1/2 = 1/3
300
The numbers 1-10 are on cards. Find the probability the card is greater than 5 or an odd number.
P(5 or odd) = 1/10 + 5/10 - 1/10 = 5/10.
300
Each gym member receives a 3-digit code to use for the lockers, with no digit repeated. Grace received the code 210. What was the probability that she received this code?
Since order matters, code 210 is unique. There are 720 ways to create a 3-digit code with no repeats. So the probability is 1/720.
400
The waiter told Kathy she can choose 3 side dishes from the 6 listed on the menu. How many groups of sides can she choose?
20
400
Two cards are drawn from the deck. What is the probability that the cards are all ACES?
P(2 Aces)= .0045
400
Use the table on lightbulb quality to answer the following: Shipped Not Shipped Defective 10 45 Not Defective 942 3 What is P( that a shipped bulb is NOT defective)?
P(shipped bulb is NOT defective) = 942/952
400
At a given high school there are 98 teachers. Of the 42 female teachers, 8 of them teach math. 1/7 of all the teachers teach math. Find P(male teacher or math teacher).
P(male teacher or math teacher) = 56/98 + 14/98 - 6/98. So the answer is 64/98.
400
Of 100 students, 37 play an instrument, 45 play sports, and 11 do both. What is the probability that a student plays neither an instrument nor plays sports?
Only 26 students play just an instrument, and only 34 play just a sport. So a total of 71 are involved in activities. This means there are 29 student not doing either. So 29/100 or 29% play neither an instrument nor a sport.
500
How many different 7-digit phone numbers can be made if the first digit cannot be 7, 8 or 9?
7,000,000 different numbers
500
Create a tree diagram to represent flipping a penny 2 times. Then, find P(tossing at least 1 Tail)
P(tossing at least 1 Tail) = 3/4
500
When playing Yahtzee you roll 5 , 5, 5, 2, 3. You decide to re-roll the 2 and 3. You can roll each die twice, hoping for 5's. What is the probability that you get no additional 5's in either of the two rolls?
No 5's for either roll means that you rolled 4 times and did not get a 5. P(not 5) = 5/6 * 5/6 * 5/6 * 5/6
500
A school survey has found that 9 out of 10 students like pizza. If you asked 3 students in the cafeteria, what is the probability that the first 2 students asked like pizza, but the third does not?
P(pizza, pizza, not pizza) = 9/10 * 9/10 * 1/10 = 81/1000.
500
There are 150 people at a play. 90 are women and 60 are men. Half are sitting in the lower level, and half are in the upper level. There are 35 women in the lower level. A person is selected for a random prize. What is the probability that the person is in the lower level, given the person is a woman?
Lower Upper Men 55 35 Women 35 55 So 35/150= .23333
M
e
n
u