test #3- Probabilities

Question 1

what is an event

Answer 1

any collection off results or outcomes of a procedure

Question 2

what is a simple event

Answer 2

an outcome that cannot be further broken down into simpler components

Question 3

what is a sample space

Answer 3

it consists of all possible simple events

Question 4

how do you calculate the number of times an event occurs

Answer 4

(#times event A occurs) x (# of times the procedure is repeated)

Question 5

what are complementary events

Answer 5

finding the probability that an event does not occur

Question 6

what is the complement of an event

Answer 6

everything but that event (A’)

Question 7

what are compound events

Answer 7

any event combining two or more simple events

Question 8

P(A or B)=

Answer 8

P(A) + P(B) - P(A and B)

Question 9

What are independent invents (with replacement)

Answer 9

when the occurence of one does not affect the occurence of the other

Question 10

what are dependent events (without replacement)

Answer 10

when the occurence of one event affects the occurence of the other

Question 11

p(A and B)=

Answer 11

P(A) x P(B)

Question 12

what is conditional probability

Answer 12

when an event’s probability is obtained with the additional information that some other has already occurred (on that condition that)

Question 13

P(A|B)=

Answer 13

P(A intersect B) / P(A)

Question 14

what are permutations

Answer 14

when different sequences of the same items are considered unique

Question 15

what are combinations

Answer 15

when different sequences of the same items are not considered unique

Question 16

fundamental counting rule;

Answer 16

(# of ways the first event occurs) x (# of ways the 2dn event occurs) (ex:how many possible codes exists with letters/numbers)

Question 17

Factorial rule;

Answer 17

n! ex: (5 students and 5 seats how many permutations?)

Question 18

permutation rule (when all items are different)

Answer 18

number of permutations when “n” items are available but only “r” are selected ex(5 students but 3 chairs)

Question 19

permutation rule (when some items are the same)

Answer 19

number of permutations when “n” items are available and selected but some items are identical

Question 20

combinations rule

Answer 20

number of different combinations when “n” items are available but only “r” are selected.

Question 21

what is a random variable

Answer 21

a variable that has a single probability for each value of x

Question 21

what is a discrete random variable

Answer 21

random variable with finite values

Question 22

what is a continuous random variable

Answer 22

random variable with infinitely many values

Question 23

what is a probability distribution

Answer 23

a description that gives the probability for each value of x of the random variable

Question 24

what are the three requirements for a probability distribution

Answer 24

1- there is a numerical random variable and its x values have a corresponding probability
2- Ep(x)=1
3- p(x) is higher than zero but smaller than 1

Question 25

what is the range rule of thumb

Answer 25

the vast majority of values lies within 2 standard deviations of the mean

Question 26

what is binomial probability distribution

Answer 26

it allows us deal with situations in which outcomes belong to one of two categories; success or failure

Question 27

what are the four requirements for binomial probability distribution

Answer 27

1- the procedure has a fixed number of trials
2-the trials must be independent
3- each trial falls into either success or failure
4- the probability of success remains the same in all trials