CS 174 Spr 99 Lecture 10 Summary
نویسنده
چکیده
Example 1 Lets consider the integers from 1 to 10,000. The properties are defined as follows: E1 = property that an integer is divisible by 4 E2 = property that an integer is divisible by 5 E3 = property that an integer is divisible by 6 The probabilities of individual divisability are easily computed: Pr [E1] = probability the number is divisible by 4 = 1=4 Pr [E2] = probability the number is divisible by 5 = 1=5 Pr [E3] = probability the number is divisible by 6 = 1=6 The probabilities for double divisibility are equivalent to divisability by the lcm of the two factors: Pr [E1 \ E2] = probability the number is divisible by 4 and 5 = 1=20 Pr [E2 \ E3] = probability the number is divisible by 5 and 6 = 1=30 Pr [E1 \ E3] = probability the number is divisible by 4 and 6 = 1=12 Finally, the probability of divisibility by all 3 factors is: Pr [E1 \ E2 \ E3] = probability the number is divisible by 4, 5 and 6 = 1=60 Substituting in the inclusion/exclusion formula:
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