The Universal Set, U, consists of the natural numbers from 20 to 60 incluive a. Define or describe in words the following three (3) sets: factors of 64, prime numbers, and multiples of 3. b. List the elements in each of your sets: A={ B={ C={ c. Determine the probability of each of the following: I.P(C) II.P(A∪B) III.P(A∩B∩C) IV.P(BC) V.P((AB)∩C)

Question

The Universal Set, U, consists of the natural numbers from 20 to 60 incluive  a. Define or describe in words the following three (3) sets: factors of 64, prime numbers, and multiples of 3.  b. List the elements in each of your sets:  A={  B={  C={  c. Determine the probability of each of the following:  I.P(C)  II.P(A∪B)  III.P(A∩B∩C)  IV.P(BC)  V.P((AB)∩C)

escumantsu · Accepted Answer

Step 1: Given:The natural numbers between 20 and 60 inclusively make up the universal set U. We must respond to the following...Step 2: Explanation:Solution (a).&amp;nbsp;Having three sets,S1=&amp;nbsp;factors of 64 i.e. 1,2,4,8,16,32,64&amp;nbsp;S2=&amp;nbsp;prime numbers&amp;nbsp;S3=&amp;nbsp;multiple of 3&amp;nbsp;Now describe the sets in words,&amp;nbsp;S1={x:x&amp;nbsp;&amp;nbsp;is a factor of 64 and&amp;nbsp;20≤x≤60}&amp;nbsp;S2={x:x&amp;nbsp;&amp;nbsp;is prime and&amp;nbsp;20≤x≤60}&amp;nbsp;S3={x:x&amp;nbsp;&amp;nbsp;is multiple of 3 and&amp;nbsp;20≤x≤60}&amp;nbsp;Solution (b).&amp;nbsp;List of the elements&amp;nbsp;S1={32}&amp;nbsp;S2={23,29,31,37,41,43,47,53,59}&amp;nbsp;S3={21,24,27,30,…,57,60}&amp;nbsp;Solution (c).&amp;nbsp;Calculate the likelihoodSince we have from the b part,&amp;nbsp;S1∪S2={32,23,29,31,37,41,43,47,53,59}&amp;nbsp;S1∩S2∩S3=ϕ&amp;nbsp;I.P(S3)=1440=720&amp;nbsp;II.P(S1∪S2)=1040=14&amp;nbsp;III.P(S1∩S2∩S3)=040=0

The Universal Set, U, consists of the natural numbers from 20 to 60 incluive Define or describe in words the following three (3) sets: factors of 64, prime numbers, and multiples of 3.

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