5 Probability FACT
1. A probability of 0 means that an event is impossible.
So if you find that P(E) = 0, that means that E will not occur.
Example:- when rolling a six-sided die,
the event that we roll a 7 is possible ?
NO 7 event is impossible.
it does not occur in any of our outcomes. Thus,
P(of 1 roll is )= 1/6
P(of 2 roll is )= 1/6
P(of 3 roll is )= 1/6
P(of 4 roll is )= 1/6
P(of 5 roll is )= 1/6
P(of 6 roll is )= 1/6
P(of 7 roll is ) = 0.
2. A probability of 1 means that an event is certain.
EXAMPLE :-So, when rolling a six-sided die,
the event that we roll some number is a certainty --
it occurs in all of our outcomes.
Thus, P(Roll a number) = 1.
3. An event with a higher probability is more likely to occur.
SO , if the probability of choices is 20% and 80% than the most higher probability of is more likely to occur that is 80%.
EXAMPLE:- if the probability of snows is 20% while the probability of rains is 80%, then it is more likely to rain than it is to snow. So, events with a lower probability are less likely to occur.
4. Probabilities are always between 0 and 1.
5. The probabilities of our different outcomes must sum to 1.
EXAMPLE:-
if we have 4 different outcomes, then
P(Outcome 1) + P(Outcome 2) + P(Outcome 3) + P(Outcome 4) = 1.
EXAMPLE:- there are six possible outcomes in die. Only 1 outcome is coming at one time by flip the die. and total outcome is 6..
Roll a "1": Probability is
Roll a "2": Probability is
Roll a "3": Probability is
Roll a "4": Probability is
Roll a "5": Probability is
Roll a "6": Probability is
And the sum of all the probabilities:
Now, for the GRE, there are three main types of probability problems:
- The probability of a single event occurring: P(A)
- The probability that two events both occur: P(A and B)
.
Using the definition of conditional probability, we find,
p(A or B) = p(A) + p(B).
