PROBABILITY

Question 1

MEASURES of CENTRAL TENDENCY $MEAN\ $ $\left(\bar{x}\right)\ $

Accepted Answer

The average of the number $\bar{x}\ =\ \frac{\sum x}{n}$

Question 2

MEASURES of CENTRAL TENDENCY $MEDIAN\ $ $\left(\widetilde{x}\right) $

Accepted Answer

The MIDDLE DATA, when ARRANGE from LEAST to GREATEST

Question 3

MEASURES of CENTRAL TENDENCY $MODE\ $ $\left(\hat{x}\right)\ $

Accepted Answer

The VALUE that APPEARS MOST FREQUENTLY in a data set

Question 4

MEASURES of CENTRAL TENDENCY $RANGE $

Accepted Answer

The DIFFERENCE between the MAXIMUM value to the MINIMUM value ${\rm Value}_{max}\ -\ {\rm Value}_{min}$

Question 5

MEASURES of DISPERSION $if\ n>30$

Accepted Answer

Population Standard Deviation $\sigma_p=\ \sqrt{\frac{\sum\left(x-\bar{x}\right)^2}{n}}$

Question 6

MEASURES of DISPERSION $if\ n\le\ 30$

Accepted Answer

Sample Standard Deviation $\sigma_s=\ \sqrt{\frac{\sum\left(x-\bar{x}\right)^2}{n-1}}$

Question 7

MEASURES of POSITION (QUANTILES) Quartiles

Accepted Answer

$Q_i=\ \frac{i}{4}\left(n\ +\ 1\right)\ $

Question 8

MEASURES of POSITION (QUANTILES) Decile

Accepted Answer

revised figure $D_i=\ \frac{i}{10}\left(n\ +\ 1\right)\ $

Question 9

MEASURES of POSITION (QUANTILES) Percentile

Accepted Answer

revised figure $P_i=\ \frac{i}{100}\left(n\ +\ 1\right)$

Question 10

DETERMINE FIRST if ARRANGEMENT is IMPORTANT or NOT IMPORTANT

Accepted Answer

IMPORTANT = PERMUTATION NOT IMPORTANT = COMBINATION

Question 11

PERMUTATION - arrangement is IMPORTANT Distinct Permutation the number of all possible arrangements or permutations of n distinct objects taken r at a time.

Accepted Answer

$n\ P\ r\ =\ \frac{n!}{\left(n\ -r\right)!}$

Question 12

PERMUTATION - arrangement is IMPORTANT Repetitive Permutation the number of all possible arrangements or permutations of n distinct objects taken r at a time with identical objects

Accepted Answer

$n\ P\ r\ =\ \frac{N!}{R!}$ N= number of obj. (counting certain identical obj as 1) R= number of how many times the certain obj repeated

Question 13

PERMUTATION - arrangement is IMPORTANT Circular Permutation total number of ways in which n distinct objects can be arranged around a fixed circle. the start and end is indistinctive

Accepted Answer

$n\ P\ r\ =\ \left(n-1\right)!$

Question 14

PERMUTATION - arrangement is IMPORTANT Circular in Space Permutation

Accepted Answer

$n\ P\ r\ =\ \frac{\left(n-1\right)!}{2}$

Question 15

COMBINATION - arrangement is NOT IMPORTANT Distinct Combination

Accepted Answer

$n\ C\ r\ =\ \frac{n!}{r!\ \left(n-r\right)!}$ n= number of choices r= number of outcomes

Question 16

COMBINATION - arrangement is NOT IMPORTANT Derangement Combination a derangement of a set leaves no element in its original place

Accepted Answer

$!n\ =n!\sum_{k=0}^{n}{\ \frac{\left(-1\right)^k}{k!}}$

Question 17

relationship between PERMUTATION and COMBINATION

Accepted Answer

$n\ C\ r=\ \frac{n\ P\ r}{r\ !}$

Question 18

PROBABILITY

Accepted Answer

$P\ =\ \frac{SUCCESSFUL\ outcomes}{total\ number\ of\ POSSIBLE\ outcomes}$

Question 19

MATHEMATICAL EXPECTATION If p is the probability that a person will receive a sum of money S, the mathematical expectation is defined

Accepted Answer

$E = pS$ p= probability of success S= sum of prize

Question 20

ODDS in FAVOR the likelihood of something occurring. It is a gambling term referring to a mathematical calculation of probability.

Accepted Answer

$Odds\ in\ Favor\ =\ \frac{SUCCESSFUL\ }{failure}$

Question 21

ODDS in AGAINST or FAILURE the likelihood of something occurring. It is a gambling term referring to a mathematical calculation of probability.

Accepted Answer

$Odds\ Against\ =\ \frac{failure\ }{SUCCESS}$

Question 22

MUTUALLY EXCLUSIVE EVENTS Two or more events are mutually exclusive , they cannot occur simultaneously.

Accepted Answer

$P\left(A\ \cap B\ \right)=\ 0$
$P\left(A\ \cup B\ \right)=\ P\ \left(A\right)\ +P\ \left(B\right)$
the probability of both events happening at the same time is zero.
For example, when tossing a coin, the result can either be heads or tails, but not both

Question 23

MUTUALLY INCLUSIVE EVENTS Two or more events are mutually inclusive, if one or the other or both can occur.

Accepted Answer

$P\left(A\ \cap B\ ight)
eq\ 0$ $P\left(A\ \cup B\ ight)=\ P\ \left(Aight)\ +P\ \left(Bight)-P\left(A\ \cap B\ ight)$ For example, the events “buying an alarm system” and “buying bucket seats” are mutually inclusive, as both events can happen at the same time

Question 24

CONDITIONAL PROBABILITY Bayes Theorem

Accepted Answer

$P\left(A|B\right) \cdot P\ \left(B\right)=\ P\left(B|A\right) \cdot P\ \left(A\right)\ =P\left(A\cap B\right)$

Question 25

BINOMIAL DISTRIBUTION
In a binomial experiment
(also called the Bernoulli trial),
there are 2 mutually exclusive outcomes often referred to as “success” and “failure”, or the probability of each trial
is not affected

Accepted Answer

$ P\ \left(x\ =r\right)=\ \left(n\ C\ r\right)\cdot\left(p^r\right)\cdot{\ \left(q\right)}^{n-r}$

n =number of trials (occurrences)
r =number of successful trials
p =probability of success in a single trial
q = (1-p)

Question 26

BINOMIAL APPROXIMATION to NORMAL DISTRIBUTION usually used in large value n to be “sufficiently large” it needs to meet the following criteria $np\geq\ 5$ $n\left(1-p\right)\geq\ 5$

Accepted Answer

$\bar{x}\ =\ np$ $\sigma\ =\ \sqrt{npq}$

PROBABILITY

All cards