Basic Probability 1 Flashcards
What are examples of chance?
- the odds of being struck by lightening - 1 in 3 million
- the odds of winning the lottery - 1 in 14 million
How is basic probability used in business?
Owner of a corner shop wants to supply newspapers. Must decide how much to buy (Q) from wholesaler at wholesaler price (W). Any unused papers cannot be sold = OC. How many should be bought? Based on previous demand as demand for newspapers realises in the day
Which 10 adjectives represent certainty?
- Certain
- Expected
- Likely
- Probable
- Not unreasonable that
- Possible
- Hoped.
- Not certain
- Doubtful
- Impossible
What is the definition of probability?
The chance that an uncertain event will occur (0-1)
What is an impossible event?
An event that has no possibility of occurring (0)
What is a certain event?
An event that is sure to occur (1)
What is priori probability?
Based on prior knowledge, we know all the possible outcomes and they are all equally likely e.g tossing a coin
How is probability occurrence calculated for a priori?
no. of ways event occurs/total possible outcomes
What is empirical probability?
Based on observed data, e.g experiments, surveys
How is probability occurrence calculated for empirical data?
no. of ways event occurs/total possible outcomes
What is subjective probability?
Based on combinations of past experiences, personal opinion, and analysis of a particular situation
How is it possible to distinguish between empirical probability and priori probability when you can conduct experiments for a priori?
If you tossed a coin several times, it would be unlikely to produce 1/2. However, if done an infinite number of times it would produce a 1/2. Probability only becomes priori after many experiments.
- For empirical experiments, you would look at number of trials rather than no. outcomes
When is subjective probability useful considering that if you ask two people you will get two different outcomes?
- No previous data
- When empirical/priori cannot be computed
What is the sample space?
Collection of all possible outcomes
What is an experiment?
Any procedure where the outcome is unknown
What are events?
Each possible outcome of a variable is an event
What is a simple event?
An event described by 1 characteristic e.g a day in January
What is a joint event?
An event described by two or more characteristics e.g a day in Jan that is also a Wednesday
What is a complement of A?
All events that are not part of event A, e.g all days in 2015 that are not January
What is marginal probability?
Refers to the probability of a simple event e.g January when given a contingency table showing 2 variables. e.g Table shows days in Jan, not Jan, Wed, not Wed but we are only interested in Jan.
What does marginal probability always correspond to in terms of a contingency table?
Always corresponds to row or column totals in a contingency table
What does joint probability correspond to in a contingency table?
Refers to values within the contingency table rather than the row or column totals.
How is the probability of joint event A and B computed?
P (A and B) = the number of outcomes satisfying A and B/total outcomes
How is the marginal probability of event A calculated when given A and B in a contingency table?
P (A) = P (A and B) + P (A1 and B2) +….+ P (A and Bk)
P (wed) = P ( wed and jan) + P (wed and feb) +…+ P (wed and dec)
NOTE - all these months are mutually exclusive and collectively exhaustive
What are mutually exclusive events?
Events that cannot occur simultaneously e.g Jan and not Jan. The joint probability of mutually exclusive events is 0 as they cannot occur together.
What are collectively exhaustive events?
If the two events cover the entire sample space. One of the events must occur. The sum of collectively exhaustive events is 1. e.g Jan and not Jan
What is the general addition rule?
P (A or B) = P (A) + P (B) - P (A and B)
P (Jan or Feb) = P (Jan) + P (Feb) - P (Jan and Feb)
What does the general addition rule mean?
The union of the two events is equal to the summation of their marginal probabilities minus their joint probability. Union is denoted by OR and joint is denoted by AND.
