Show:
Vocabulary
Probability
Odds
Permutations
Combinations
100
the arrangement of objects where the order is not a consideration
combination
100
There are 28 students in class. 16 are girls, and 12 are boys. Find the probability that a student selected at random will be a girl.
16/28 (or 4/7, or .571)
100
If a coin is thrown, what are the odds that it will turn up “tails”?
(1/2)/(1/2) = 1 :: 1 = even odds, 1 to 1
100
In how many ways can six girls be arranged in a straight line?
6! = 720
100
How many groups of size six can be selected from 6 boys?
one Why?
200
the measure of the chance of a desired outcome happening
probability
200
If a coin is thrown, what is the probability that it will turn up “tails”?
1/2
200
There are 28 students in class. 16 are girls, and 12 are boys. Find the odds that a student selected at random will be a girl.
(16/28)/(12/28) = 16/12 = 4/3 The odds of a girl are 4 to 3 in favor of a girl.
200
In how many ways can 4 classes be arranged on your schedule, if you have 20 classes to choose from?
20 Pr 4 = 20!/ (20 - 4)! = 116,280
200
How many groups of size 3 can be selected from 6 boys?
6 C 3 = 20 = 6!/(3!3!)
300
events that do not affect each other
independent events
300
Four marbles are removed at random from a bag containing five orange and seven brown marbles. What is the probability that all four marbles are orange?
(5/12)(4/11)(3/10)(2/9) = 1/99
300
Four marbles are removed at random from a bag containing five orange and seven brown marbles. What is the probability that all four marbles are orange?
Odds (4 Orange) = 1 to 98 in favor of 4 Oranges = 1:98
300
How many distinct permutations can be made using all the letters of the word: assassination
13!/(4!3!2!2!) = 10,810,800
300
How many groups of 4 classes can be included on your schedule, if you have 20 classes to choose from?
20 C 4 = 4,845 = 20!/(17!4!)
400
sample space
the set of all possible outcomes of an event
400
A) List a sample space to show all possible outcomes when a family has three children. B) What’s the probability of the family having 2 girls and one boy?
A) Sample Space = S = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG} B) P(2G & 1B) = 2/8 = 1/4 =.25 [Note; BGG, GGB]
400
A bag contains 24 balls. Five of the balls are red, four are green, seven are blue, and eight are yellow. What are the odds that a ball picked at random will be red?
5/19 Why?
400
In how many ways can six girls be arranged in a circle?
5! = 120 remember for a circle with no fixed point established, it is (n-1)!
400
A store has 7 different ties for sale. If the manager wants to display a combination of four of these ties by the checkout, what is the number of possible combinations?
7 C 4 = 35 = 7!/(3!4!)
500
tree diagram
a diagram used to show the total number of possible outcomes of an event
500
If three cards are drawn at random from a deck of 52 cards, what is the probability that they are all spades?
(13/52)(12/51)(11/50) = 33/255
500
Three people are going to be chosen for senior representatives. What are the odds of 3 boys being chosen out of 6 girls and 10 boys?
The odds are 3/11 Solution: P(3 Boys)= (10/16)(9/15)(8/14) = 3/14, so P(not 3 Boys) = 11/14 & Odds in favor of 3 Boys = 3:11
500
a) Explain the difference between a combination and a permutation. b) If you select 5 of 17 possible choices, which is greater? The # of Permutations or the # of Combinations? c) Why is this true?
a) Combinations are the number of unique groups we can select, while permutations are the number of uniquely ordered arrangements possible for each of these groups. b) Hence # permutations > = # combinations, always c) For any combination there are one of more different orders possible for the elements in the combination
500
Find the possible number of license plates consisting of 2 letters followed by 4 digits if digits can be repeated but letters cannot.
26*25*10^4 = 650*10^4 = 6,500,000 = 6.5 million