Question

Evaluate and provide examples of the differences between using the general addition rule and conditional probability. In what situations are the approaches most applicable? Provide an example of appropriate use of each approach.

Answer 1

General Addition Rule : When two events, A and B, are mutually exclusive, the probability that A or B will occur is the sum of the probability of each event.

For example - From the set {1,2,3,4,5,6,7,8,9,0} probability of selecting {1} and {2} is the sum of individual probability.

Solution:

P({1}) = 1/10 .  P({2}) = 1/10

P({1,2}) = 1/10

The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred. This probability is written P(B|A), notation for the probability of B given A. In the case where events A and B are independent (where event A has no effect on the probability of event B), the conditional probability of event B given event A is simply the probability of event B, that is P(B).

For example:- In an exam, two reasoning problems, 1 and 2, are asked. 35% students solved problem 1 and 15% students solved both the problems. How many students who solved the first problem will also solve the second one?
Solution:
Probability of student solving problem 1,P(1)=0.351
Probability of student solving both problem, P(1 and 2) = 0.15
Probability of solving 2 if 1 is solved, P(2|1)P(2|1) = P(1and2)/P(1) = 0.15/0.35 = 0.428

From above two definitions and examples we can get the situations when we should apply addition rule or conditional.

So for condition - if we have to find the probability of an event which will occur given that another event has occurred we will use these.

For addition - When two events are mututally exclusive, we will use these.