Probability

Question 1

P(E) is ?

Answer 1

P(E) is the probability of the event, E, occurring where if E can occur in h ways out of a total of t possible ways then P(E) = h/t

Question 2

Independent vs. dependent events

Answer 2

independent events are within a set where one event can occuring without affecting the occurence of other, later events. If one event changes the probability of other events then the set is dependent

Question 3

Mutually exclusive events

Answer 3

This means that one event occurring obscures the ability for any other event to occur at that moment. P(E₁ ∩ E₂) = 0

Ex: The probability of drawing both an ace and a king in one draw is zero

Question 4

Probability of two independent events simultaneously occurring

Answer 4

If E₁ and E₂ are independent then P(E₁ ∩ E₂) = P(E₁) * P(E₂)

Question 5

Permutation

Answer 5

This is the number of different configurations that a number of dependent events (x) can take out of a total number of options (n)

This is denoted by _nP_x = n!/(n-x)!

Question 6

How many different arrangements can 5 cards of a normal deck have if drawn at once?

Answer 6

₅₂P₅ = 52!/(52-5)! = 311875200 This is the total number of possible permutations

Question 7

Combinations

Answer 7

This represents the number of ways different dependent elements can be arranged if selected during one event.

_nC_x = n! /(n-x)!*x!

Question 8

Standard deviation formula and meaning

Answer 8

This is a measure of dispersion and is given by S = [(Σ (x_i - x_a)²)/(n-1)]^.5

Question 9

Z score

Answer 9

Z= (x-μ)/σ = the number of standard deviations that x is from the population mean