Understanding Probability: Fundamentals, Applications, and Real-World Examples

Presentation:
https://www.youtube.com/watch?v=PfHoz36jpcI

This presentation provides a comprehensive introduction to probability, the branch of mathematics that deals with the likelihood of events occurring. It covers key concepts such as probability rules, types of probability (theoretical, experimental, and conditional), probability distributions, and real-world applications in fields like finance, science, and decision-making.

With clear explanations and practical examples, this guide is ideal for students, educators, and professionals looking to strengthen their understanding of probability theory and its significance in everyday life.

1. Probability

2. Marcel David Baroi ID: 201-15-3421 CSE

3. Probability Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur Probability of an event is a number between 0 and 1. 0 indicates impossibility of the event and 1 indicates certainty Probability of event to happen P(S) = P(S) =  

4. Example 1: What is the probability that we get an even number from a dice? All possible Outcomes\ Sample space Favourable outcomes P(S) =   n(S) = 6 n(A) = 3

5. Example 2: A fair coin is tossed three times. What is the probability that at least one head appears? Solution: Samples S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} n(S) = 8 Favorable outcomes A = {HHH, HHT, HTH, THH, HTT, THT, TTH} n(A) = 7 P(A) =  

6. Ace 2 3 4 5 6 7 8 9 10 Jack Queen King Clubs Diamonds Hearts Spades 13 13 13 13 52 Standard 52-card deck

7. Example 3: A card is drawn from an ordinary deck of 52 playing cards. Find the probability of Card is a red card Card is a Dimond Card is 10 Solution Here n = 52 I. Let A represent the event that card is a red card P(A) = II. Let B represent the event that card is a Dimond card P(B) = III. Let a represent the event that card is a 10 P(A) =  

8. ABCD Arrange and combine two of the four letters AB BA CA DA AC BC CB DB AD BD CD DC Permutation Combination Ordered subset of set on n P = 12 Set of r objects selected without their order Permutation Combination Ordered subset of set on n Set of r objects selected without their order P = 12 C = 6

9. Permutation Combination Ordered subset of set on n P = 12 Set of r objects selected without their order Permutation Combination n P r  =   n C r  =   Permutation =   Combination =  

10. Example 4: 6 white balls and 4 black balls which are indistinguishable apart from color are placed in a bag. If 6 balls are taken from the bag, find the probability of their being three white and three black. Solution Here, T otal balls = 10 White balls = 6 Black balls = 4 Let six balls are selected at random from ten balls. The possible number if outcomes in which 6 balls are selected from 10 balls n(S) = 10 C 6 =   Let A denotes the event that three balls are white and three black n(A) = 6 C 3 × 4 C 3 =   Therefore, P(A) =  

11. Special thanks Md. Arifuzzaman Senior Lecturer (Mathematics) Department of General Educational Development (GED) Daffodil International University

12. (Thankyou) ∞