Concept of Conditional Probability

Conditional Probability:

Remember that the probability of an event occurring given that the other event has already occurred is termed as a conditional probability.

The probability which event B takes place, given that event A has already occurred is:

P(B|A) = P(A and B)/P(A)

The above formula is derived from the general multiplication principle and a little bit of algebra.

As we are given that the event A has occurred, we have a decreased sample space. Rather than the whole sample space S, we now contain a sample space of A as we know A has occurred. Therefore the old rule about being the number in the event divided by the number in sample space still applies. This is the number in A and B (should be in A as A has occurred) divided by the number in A. When divided numerator and denominator of the right hand side by the number in sample space S, then we have the probability of A and B divided by the probability of A.

Example: The question, ‘Do you smoke?’ was asked of 100 people. The outcomes are shown in the table below.


                Yes    No     Total
Male         19     41      60
Female     12     28      40
Total         31     69     100

1) Find out the probability of a randomly chosen individual being a male who smokes?

This is simply a joint probability. The number of Male and Smoke divided by the total = 19/100 = 0.19

2) Find out the probability of a randomly chosen individual being a male?

This is a total for male divided by the total = 60/100 = 0.60. As no mention is made up of smoking or not smoking, it comprises all the cases.

3) Find the probability of a randomly chosen individual smoking?

Again, as no mention is made of gender, this is the marginal probability, the total who smoke divided by the total = 31/100 = 0.31.

4) Find out the probability of a randomly chosen male smoking?

This time, you are told that you encompass a male - think of stratified sampling. Determine the probability that the male smokes? Well, 19 males smoke out of 60 males, therefore 19/60 = 0.31666...

5) Find out the probability that a randomly chosen smoker is male?

This time, you are told that you encompass a smoker and asked to determine the probability that the smoker is as well male. There are 19 male smokers out of 31 total smokers, therefore 19/31 = 0.6129

Latest technology based Statistics Online Tutoring Assistance

Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Statistics help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Statistics, project ideas and tutorials. We provide email based Statistics help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Statistics. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Statistics Homework help and assignment help services. They use their experience, as they have solved thousands of the Statistics assignments, which may help you to solve your complex issues of Statistics. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.