1. Introduction to probability (3) Definition: - The probability of an event A is the sum of the weights of all sample point in A therefore If A1,A2,…..,An is a sequence of mutually exclusive events then

2. Introduction to probability (3) Rule: If an experiment can result in any one of N different equally likely outcomes and if exactly n of these outcomes correspondent to event A, then the probability of event A is

3. Introduction to probability (3) Examples 1. A balanced coin tossed twice what is the probability that at least 1 head occurs. Solution: The number of ways for this experiment is ways. Then the sample space is, N =4 The event of at least 1 head occurring. n=3.

4. Introduction to probability (3) 2. A die is loaded in such a way that an even number is twice as likely to occur as an odd number. If (E) is event that the number less than 4 occurs in a single toss of the die. 1. Find P(E) The sample space is Now we assign a probability of w to each odd number and a probability of 2w to each even number. Then, N= 9w.

5. Introduction to probability (3) E= {1, 2, 3} < 4 P (E) = {w, 2w, w} b. Let A be the event that an even number turns up and let B be the event that a number divisive by 3 occurs. Find and.

6. Introduction to probability (3) Solution: Event A is {2, 4, 6}, event B is {3, 6}.

7. Introduction to probability (3) 3. A statistics class for engineers consists of 25 industrial, 10 mechanics, 10 electrics an 8 civil engineering students. If a person is randomly selected by instructor to answer the question. Find the probability that the student chosen is: a) An industrial engineering major. b) Civil engineering or an electrical engineering. c) Mechanics and electrical engineering.

8. Introduction to probability (3) Solution: Let I: denotes for industrial engineering. M: denotes for mechanics engineering. E: denotes for electrical engineering. C: denotes for civil engineering. N:= sum of student at class room. N = 25 + 10 + 10 + 8 = 53 students. a. Since 25 of 53 students are majoring industrial engineering. Then the probability of event I selecting an industrial engineering major at random is:

9. Introduction to probability (3) 1. 2. 3. Then the probability a civil engineering or electrical engineering is:

10. Introduction to probability (3) 4. In a poker hand consisting of 5 cards, find the probability of holding 2 aces and 3 Jacks. Solution: The total number of 5 cards hands all of which are equal is

11. Introduction to probability (3) And Now there are hands with 2 aces and 3 Jacks

12. Introduction to probability (3) Then the probability of getting 2 aces and 3 Jacks in a 5 cards poker P(C) is