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Probability (5) probability of event with finite S

Probability (5) probability of event with finite S -...

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Probability of an event with a finite sample space having equally likely outcomes
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Example } 6 { } 5 { } 4 { } 3 { } 2 { } 1 { 6 6 6 6 6 = S Consider a fair die. What is the probability that the outcome is divisible by 3? . 6 , , 2 , 1 , 6 1 }) ({ = = i for i P Fair 1, 2, 3, 4, 5 and 6 occur equally likely
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Example }) 6 ({ }) 3 ({ }) 6 , 3 ({ ) ( P P P A P + = = } 6 { } 3 { } 6 , 3 { 6 = = A Consider a fair die. What is the probability that the outcome is divisible by 3? Let A be the event that the outcome is divisible by 3 By the third axiom of a probability, 6 2 6 1 6 1 = + =
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Example Consider a fair die. What is the probability that the outcome is divisible by 3? If we denote the number of elements in an event B by n(B), then n(S) = 6 , n(A) = n({3,6}) = 2 , and n({i}) = 1, for i=1,2,…,6. }) 6 ({ }) 3 ({ }) 6 , 3 ({ ) ( P P P A P + = = 6 2 6 1 6 1 = + = n(A) n(S)
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If the sample space for an experiment contains finite, say N, elements , all of which are equally likely to occur , then the probability of any event A, denoted by P(A), containing n of these N sample points is the ratio of the number of elements in A to the number of elements in S , i.e. . ) ( N n A P =
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Questions Toss a fair die. Let A be the event that an odd number turns up and B be the event that the turning-up number is a prime number .
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