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INTRODUCTION TO PROBABILITY.pptx
This document provides an introduction to probability. It defines key probability terms like certain, likely, equally likely, unlikely, and impossible. It explains how to calculate the probability of an event using the formula: Probability (P) = Number of favorable outcomes / Total number of possible outcomes. It provides examples of calculating probabilities for events like drawing cards from a deck or numbers on a clock. It concludes with several word problems asking the reader to calculate probabilities based on the information provided.
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INTRODUCTION TO PROBABILITY.pptx
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- 4. Tossing a coinRolling a dice Have two possibilities Have six possibilities Head or Tail Getting 1, 2, 3, 4, 5, 6
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- 11. Terms used in Probability •Certain • Likely • Equally likely • Unlikely • Impossible
- 12. Note: • For anEvent E to occur: • Certain means 100% chances. • Likely means more chances • Unlikely means less chances • Equally Likely means 50% chances • Impossible means No chance at all ( 0 % chances)
- 13. Likely… • More vsLess Likely
- 15. Exhaustive Events: • Inprobability, a set of events is collectively exhaustive if they cover all of the probability space: i.e., the probability of any one of them happening is 100%. If a set of statements is collectively exhaustive we know at least one of them is true.
- 16. Mutually Exclusive Events •Disjoint events, events that don’t have anything in common. • Non-Mutually Exclusive Events are also called Mutually Inclusive events. Mutually Exclusive Events:
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- 27. PROBABILITY RULES • P(E)= 𝑷 𝑬 = 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒇𝒂𝒗𝒐𝒖𝒓𝒂𝒃𝒍𝒆 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒕𝒐𝒕𝒂𝒍 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔 • P( Not E) = 1 – P(E) • For any event E, 𝟎 ≤ 𝑷 𝑬 ≤ 𝟏. • P(E) = 0 if and only if E is an impossible event. i.e. it will Never occur. • P(E) = 1 if and only if E is a certain event. i.e. it will Definitely occur
- 29. Ques:01 • A cardis drawn at random from a standard pack of 52 playing cards. • Find the probability of drawing : • 1. E = a red card • 2. E = an ace • 3. E = the three of clubs (3 of club) • 4. E = a card which is not the three of clubs
- 30. Ques:02 • Two jokercards are added to a standard pack of 52 playing cards. A card is then drawn at random from the 54 cards. Find the probability of drawing • (i) a red card (ii) a two • (iii) a joker (iv) a queen or a king • Note: A Joker card is neither a black or red card.
- 31. Ques:03 • Raj wakesup in the morning and notices that his digital clock reads 07:25. (ST:AB) • At noon, he looks at the clock again. What is the probability that • (i) the number in column A is a 4? • (ii) the number in column B is 8? • (iii) the number in column A is less than 6. • (iv) the number in column B is greater than 5?
- 32. Solution: • A ={0, 1, 2, 3, 4, 5} • B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} • (i) the number in column A is a 4? P(E) = 1/6 • (ii) the number in column B is 8? P(E) = 1/10 • (iii) the number in column A is less than 6. P(E) = 6/6 = 1 • (iv) the number in column B is greater than 5? P(E) = 4/10 = 2/5
- 33. Ques:04 • There area total 117 pairs of socks in a clothes bin. Each pair of socks is placed in a bag. The probabilities of selecting a yellow pair of socks and a grey pair of socks at random from the bin are 2/9 and 3/13 respectively. Find the number of pairs of socks in the bin which are • (i) yellow, • (ii) neither yellow nor grey.
- 34. Ques:05 • A cartoncontains 15 toothbrushes, out of which p have soft bristles. After 5 more toothbrushes of soft bristles are added to the carton, the probability of drawing a toothbrush with soft bristles becomes ¾. Find the value of p.
- 35. Ques:06 • There are50 students in an Auditorium, of which 2x are boys and y are girls. After (y – 6) boys leave the Auditorium and (2x – 5) girls enter the Auditorium, the probability of selecting a girl at random becomes 9/13. Find the value of x and y.