Ch. 4: Probability and Probability Models Flashcards
deals with uncertainty; measures the chance of likelihood that an event will occur
probability
(ex: whether the football team will win or not)
Probability is always between ___ and _____.
0 (low probability) and 1 (high probability)
any process of observation with an uncertain outcome
experiment
the possible outcomes for an experiment are called the _______ ________
experimental outcomes (results)
a measure of the chance that an experimental outcome will occur when an experiment is carried out
probability
the ________ ______ of an experiment is the set of all possible experimental outcomes.
sample space
(ex: we are tossing a coin, with one side heads (H) and one side tails (T). The sample space would be: {H,T})
the experimental outcomes in the sample space are called….
sample space outcomes
Sample space is called ____ for short.
S
How do we write the probability of something?
P(E)
(If E is an experimental outcome, then P(E) denotes the probability that E will occur)
What are the 2 conditions for probability?
- 0 ≤ P(E) ≤ 1 such that:
- If E can never occur, then P(E)=0
- If E is certain to occur, then P(E)=1
(aka probability is always between
0 and 1)
- The probabilities of all the experimental outcomes must sum to 1.
What are the 3 methods to assigning probabilities to sample space outcomes?
- Classical Method
- Relative Frequency Method
- Subjective Method
Match the following to the methods they describe for assigning probabilities to sample space outcomes:
a.) assessment based on experience, expertise or intuition.
b.) for equally likely outcomes.
c.) using the long run relative frequency.
a.) subjective method
b.) classical method
c.) relative frequency method
Which method would you use for the following example (subjective, classical, or relative frequency)?
Tossing a two sided coin, one side with heads and one side with tails.
Classical
(equally likely to land on heads or tails. P(H)= 1/2 and P(T)= 1/2.
(another example would be rolling a dice. Each number has a 1/6 probability of being rolled)
T or F: For the Classical Method, if there are N equally likely sample space outcomes, then the probability assigned to each sample space outcome is 1/N.
True
Which method would you use for the following example (subjective, classical, or relative frequency)?
Tossing a coin 100 times, or 1,000, or 10,000 times.
Relative Frequency (do the same thing over and over)
(look at camera roll for more info)
Which method would you use for the following example (subjective, classical, or relative frequency)?
There is an 80% chance ABC company will make 60% profit. This is known based on experience.
Subjective method
a mathematical representation of a random phenomenon
probability model
a variable whose value is numeric and is determined by the outcome of an experiment
random variable
a probability model describing a random variable
probability distribution
What are the 2 types of probability distributions you can have?
- Discrete probability distributions (Ch. 6)
- Continuous probability distributions (Ch. 7)
What are the 2 types of discrete probability distributions?
what are the 3 types of continuous probability distributions?
Discrete:
1. Binomial distribution
2. Poisson distribution
Continuous:
1. Normal distribution
2. Exponential distribution
3. Uniform distribution
- An _______ is a set of sample space outcomes.
- The probability of an event is the ______ of the probabilities of the sample space outcomes.
- event
- sum
T or F: If all outcomes equally likely, the probability of an event is just the ratio of the number of outcomes that correspond to the event divided by the total number of outcomes.
True
Suppose that when we roll a dice, the sample space is: {1,2,3,4,5,6}. If asked what’s the probability you will have 5 or 6, this means you will ______ the probabilities.
ADD (remember: or means add)
= P(5) + P(6)
= 1/6 + 1/6
= 2/6 → 1/3
