Business Analytics > Probability, Risk & Sampling > Terms of Probability

Terms of Probability

Experiment: An experiment is a process that results in an outcome. An experiment might be as simple as rolling two dice, observing and recording weather conditions, conducting a market research study, or watching the stock market. The outcome of an experiment is a result that we observe; it might be the sum of two dice, a description of the weather, the proportion of consumers who favor a new product.

Example: Suppose you are observing customers buy or not buy any one of the products you have in your shop. this is an experiment. if you observe it several times (n) then it is also an experiment.

Sample Space: The collection of all possible outcomes of an experiment is called the sample space. For instance, if outcomes for customer reaction to a new product in a market research study would be favorable or unfavorable or no comment.

Event: An event is a collection of one or more outcomes from a sample space.

Examples of events are rolling a sum of 7 or 11 with two dice, completing a computer repair in between 7 and 14 days.

Complementary Events: A complementary event is an event that includes all outcomes in which the original event does not occur.

If the probability of rain today is 0.3, then the probability that it does not rain is:

P(no rain)=1−0.3=0.7

So, the complementary event of “rain” is “no rain.”

Union of Events: The union of events refers to the event that at least one of two or more events occurs. If A and B are two events, their union is written as A ∪ B.

A∪B={outcomes that are in A or in B or in both}

Example: Event A: Getting an even number when rolling a die = {2, 4, 6} and event B: Getting a number greater than 4 = {5, 6}

A∪B={2,4,5,6}

Mutually Exclusive Events: Mutually Exclusive Events are events that cannot happen at the same time. If one event occurs, the other cannot.

Example: In tossing a coin, let event A = getting “Heads” and event B = getting “Tails”
These events are mutually exclusive because a coin cannot show both heads and tails at the same time.

Another Example: Suppose an insurance sales officer is looking for customers who will buy a policy. He may visit 5 customers. Then the sample space is all possible outcome (Not Buy, Not Buy). And the experimental outcome may like: Buy, Not Buy, Not Buy, Not Buy, Buy.

Since he is looking for customer who will “Buy” , event is A= Buy. Let the complementary event is B =”Not Buy”. Here A and B are mutually exclusive events.

Considering events in his experiment as A= “Buy” B= “Male”. Naturally, some customers may posses both the properties. The experimental outcome may like:

(Asad.   - Buy:Male),

(Shahin - Not Buy:Male) ,

(Urmi.   - Not Buy: Female),

(Nasima- Not Buy:Female,

(Badrul  - Buy:Male)

Prev

Types of Probability

Next

Rules on Probability

Feedback

Submit