Your SlideShare is downloading. ×
Pai Edusat 223
Upcoming SlideShare
Loading in...5

Thanks for flagging this SlideShare!

Oops! An error has occurred.

Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Pai Edusat 223


Published on

Published in: Education

  • Be the first to comment

  • Be the first to like this

No Downloads
Total Views
On Slideshare
From Embeds
Number of Embeds
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

No notes for slide


  • 1. THE AXIOMATIC APPOACH Let for every event A, a real number P(A) be assigned. Then, P(A) is the probability of event A, if the following axioms are satisfied. Axiom 1: P(A) ≥0 Axiom 2: P(S) = 1, S beings the sure event Axiom 3: For two mutually excusive events A and B
  • 2. ADDITION THEOREM PROBABILITY For two events A and B, Show that Solution: For events A and B, ---Result 1 Here, A∩B and A`∩B are mutually exclusive. Therefore, by axiom 3, A B S Contd
  • 3. Also, By result 1 and result 2 -------Result 2 Here, A∩B and A`∩B are mutually exclusive therefore, ADDITION THEOREM PROBABILITY
  • 4. PERMUTATION& COMBINATION Problems:1. There are 20 persons. 5 of them are graduates. 3 persons are randomly selected from these 20 persons. Find the probability that at least one of the selected person is graduate. ANS 0.6
  • 5. PROBLEMS:2. In a college, there are five lecturers. Among them, three are doctorates. If a committee consisting three lecturers is formed , what is the probability that at least two of them are doctorates ? ANS 0.7
  • 6. PROBLEMS:3 What is the probability that there will be 53 Sundays in a randomly selected (i) leap year (ii) non-leap year? ANS P[ leap year has 53 Sundays]= 2/7 P[ non-leap year has 53 Sundays}= 1/7
  • 7. CONDITIONAL PROBABILITY Let P(A)>0. Then, conditional probability of event B given A is defined as - If P(A) = 0, the conditional probability is not defined.
  • 8. INDEPENDENT EVENTS Two events A and B are independent if and only if
  • 9. MULTIPLICATION THEOREM Let A and B be two events with respective probabilities P(A) and P(B). Let P(B/A) be the conditional probability of event B given that event A has happened. Then, the probability of simultaneous occurrence of A and B is – If the events are independent, the statement reduces to - Contd
  • 10. MULTIPLICATION THEOREM Proof : By the definition of conditional probability, for P(A)>0, If A and B are independent, by the definition of independence,
  • 11. PROBLEMS:1 The probability that a contractor will get a plumbing contract is 2/3 and probability that he will not get an electrical contract is 5/9. If the probability of getting at least one of these contracts is 4/5, what is the probability that he will get both? ANS 0.1352
  • 12. PROBLEMS:2 A problem in statistics is given to five students. A, B, C, D and E. Their chances of solving it are 1/2, 1/3, 1/4, 1/5 and 1/6. What is the probability that the problem will be solved?