Question

Difference between dependent and independent events in probability

Answer 1

Answer:

Independent events: events where an outcome of one event is NOT affected by the outcome of another event.

Dependent events: events where an outcome of one event IS affected by the outcome of another event.

Step-by-step explanation:

Experimental probability is when you determine the occurrences of a favorable outcome that actually happened in your experiment divided by the number of all possible outcomes. An example would be tossing a coin 50 times. Let's say you get 35 heads and 15 tails. The experimental probability of landing on a head is 35/50 = 70% and the experimental probability of landing on a tail is 15/50 = 30%. These are experimental probabilities because 35 heads and 15 tails were the actual results you got when tossing a coin 50 times. Experimental probabilities can change when you do an experiment multiple times, getting different results.

I explained independent and dependent events in the first part. The probability of two events occurring together are different depending on wether they are independent or dependent.  

P(A and B) if A & B and independent = P(A) * P(B).

P(A and B) if A & B and dependent = P(A) * P(B given A has already happened) = P(A) * P(B | A)

Examples from the business environment:  

Independent events: Customers going to a restaurant in Georgia and customers going to a restaurant in California

Dependent events: Company A has two different services. You can only choose one: Service X or Service Y. Choosing X and choosing Y: these events are dependent because the choice of one service guarantees that you cannot choose the other one.

Additional examples:  

XYZ Company has 5 different services. You can choose as many services as you like in any combination. Choosing service 1 and service 2, 3, 4, 5 are independent events.  

ABC Company has 3 services. You must choose Service 1 if you choose Service 2 and 3. Choosing Service 1 and service 2 are dependent events.