Lesson 4 Probability1

# Lesson 4 Probability1 - Probability Let S be the sample...

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Probability Let S be the sample space of an experiment in which all outcomes are equally likely and let E be an event, the probability of E , written P(E), is : The probability of an event is the sum of the weights of all sample points in E; thus, since then, . If P(E) = 0 then the event E is said to be an impossible event. If P(E) =1 then the event E is said to be a certain event. P ( E ) = n ( E ) n ( S ) = no . of elements of E . of elemens of S 0 n ( E ) n ( S ) 0 P ( E ) 1

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Theorems on Probability 1. 1. P(S) = 1 2. If n(E) = 0 then P(E)=0. 3. If A and B are mutually exclusive events then 4. If is a sequence of mutually exclusive events then 6. If A’ is the complement of an event A then P(A’) = 1 – P(A). 1. If A and B are any two events then . 2. If A and B are any two events then 3. For any events A , B, and C 0 P ( E ) 1 P ( A B ) = P ( A ) + P ( B ) A 1 , A 2 ,..., A n P ( A 1 A 2 ... A n ) = P ( A 1 ) + P ( A 2 ) + + P ( A n ) P ( A - B ) = P ( A ) - P ( A B ) P ( A B ) = P ( A ) + P ( B ) - P ( A B ) P ( A B C ) = P ( A ) + P ( B ) + P ( C ) - P ( A B ) - P ( A C ) - P ( B C ) + P ( A B C )
Examples 1. If a letter is chosen at random from the English alphabet, find the probability that the letter: a. is a vowel b. is listed somewhere ahead of the letter j c. Is listed somewhere after the letter m. 2. Interest centers around the life of an electronic component. Suppose it is known that the probability that the component survives for more than 6000 hours is 0.42. Suppose also that the probability that the component survives no longer than 4000 hours is 0.04. a. What is the probability that the life of the component is less than or equal to 6000 hours? b. What is the probability that the life is greater than 4000 hours?

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Examples 3. If a committee of 5 is selected from a group of 8 seniors, 6 juniors, and 4 sophomores, find the probability that the committee has: a. 2 seniors, 2 juniors and 1 sophomore b. No seniors c. At least one senior 4. The probability that an American company relocates in Shanghai is 0.7, the probability that it relocates in Beijing is 0.4, and the probability that it relocates in either Shanghai or Beijing or both is 0.8. What is the probability that the company will relocate in: a. in both cities?
Examples 5. In a poker hand consisting of 5 cards, find the probability of holding: a. 3 aces b. 4 hearts and 1 club 6. In a high school graduating class of 100 students, 54

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## This note was uploaded on 07/31/2011 for the course MATH 30 taught by Professor Teodoro during the Spring '11 term at Mapúa Institute of Technology.

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Lesson 4 Probability1 - Probability Let S be the sample...

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