Help I can't understand the difference between the two types of probability😩

I'd really appreciate it if someone could explain the difference between the types of probability in maths? 😊

This Q is probably GCSE in which case you are having to deal with "Mutually exclusive" events where only one can happen. e.g. select a sock and it is either blue or red, not both. This kind of question requires you to add together probabilities to answer questions of the form "What is the probability of event A OR event B happening.

if it is GCSE then OP is most probably referring to With Replacement vs Without Replacement ?

This Q is probably GCSE in which case you are having to deal with "Mutually exclusive" events where only one can happen. e.g. select a sock and it is either blue or red, not both. This kind of question requires you to add together probabilities to answer questions of the form "What is the probability of event A OR event B happening.

You also have "Independent" events where you ask about two events that might both occur. e.g. Throw a die twice and you might get 6, 6. This allows us to ask what is the probability of Event A AND Event B happening. e.g. What is the probability that you select a red top AND a blue sock

The most tricky GCSE questions often involve Tree diagrams and distinguishing with and without replacement but it is the interpretation that is most tricky and this question was well publicised. It is possible for "Mutually exclusive" events and
"Independent" events to be combined in the same long question.



If you are doing A-level then you may also have to do Bayesian probability which is more tricky to understand and involves the sample space being altered by a prior event.