Probability Flashcards
Probability of an event x
total number of outcomes in the experiment
Sample Space
set of all possible outcomes
Probability of a sample space
1
Complementary event
two events that do not occur together; if one occurs the other one doesn’t
P(A)+P(Not A)
1
P(Not A)
1- P(A)[
And in probability
multiply
Two events A and B are independent
if the fact that event A occurs does not change the probability that B will occur and vice-versa
P(A and B)
P(A) * P(B)
Dependent events
if the occurrence of the first event affects the occurrence of the second event in such a way that the probability of the second event is changed
P(A and B)
P(A) * P(B|A)
Mutually exclusive
if the can not occur at the same time
Addition rule concerning mutually exclusive events
P(A) + P(B)
P(A or B)
P(A) + (B)- P(A and B)
When an event has more than one possible outcome, each possible outcome must be considered when calculating the probability that the event will occur. Thus, to determine the actual probability we do the following
number of outcomes producing the event * probability of one outcome
*The shortcut can be used when each of the outcomes has the same probability
At least
equal to or greater to
Calculating at least probability problems
1) Define the scenarios
2) Calculate the probability of each scenario
3) Add together the probability of each scenario
When a question asks for the probability that “at least 1” outcomes will occur, consider using
complementary events to simply the problem/
P(at least 1 outcome occurs)= 1- P(none of these outcomes occur)
Two events that are not complementary
do not add up to 1
Dependent probability with multiple outcomes, consider using the/formula
Probability of an event=
number of favorable outcomes
———————————————
total number of outcomes
combination method in which you separately calculate the numerator and denominator of
Some items will or must be selected
#of ways that some numbers of items must be selected ------------------------------------------------------------------- # of ways that all items can be selected
Favorable outcomes/ total outcomes (when some items must not be selected)
#of ways that some number of items must not be selected ---------------------------------------------------------------------------- #of ways that all items can be selected
When determining the number of ways that some number of items must not be selected
mentally eliminate from the main pool those items that are excluded from the subgroup. Remember restricting item from a subgroups does not change the number of spots available in that subgroups
Probability is
a ratio
i.e: 1/4 -> there are x occurrence for every 4 occurrence
