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In a the Rules to the question. Do data were obtained in response you like the food served at Kennedy Union? Yes No No opinion Class 25 Freshman Sophomores Upperclassmen 10 7 If a student is selected at random, find these probabilities. a) The student has no opinion. b) The student is a freshman or is against the issue. c) The student is a sophomore or upperclassmen. d) The student is a sophomore or has no opinion. A recent survey on credit cards was conducted, and the results are shown in the following table. Does not Employment Own Credit Card Credit Card Employed 18 Unemployed If a person is selected at random, find these probabilities. e) The person owns a credit card, given that the person is employed. The person is unemployed, given that the person owns a credit card.Explanation / Answer
Q-5
Part-a
P(no opinion)=(8+5+2)/(25+15+10+1+4+7+8+5+2) =0.194805195
Part-b
P(Freshman or against the issue)
=P(Freshman)+P(against the issue)-P(Freshaman and against the issue)
=(25+1+8)/(25+15+10+1+4+7+8+5+2) +(1+4+7 )/(25+15+10+1+4+7+8+5+2)
- (1)/(25+15+10+1+4+7+8+5+2)
=0.584415584
Part-c
P(Sophomore or upperclassmen)=(15+4+5+10+7+2)/( 25+15+10+1+4+7+8+5+2)
=0.558441558
Part-d
P(sophomore or no opinion)
=P(sophomore)+P(no opinion)-P(no opinion)
=(15+4+5)/(25+15+10+1+4+7+8+5+2) +(8+5+2 )/(25+15+10+1+4+7+8+5+2)
- (5)/(25+15+10+1+4+7+8+5+2)
=0.441558442
Part-e
Let n() denote number of elements in event
P(own credit card/employed)=n(own credit card and employed)/n(employed)
=18/(18+29)
=0.382978723
Part-f
P(Unemployed/own credit card)=n(Unemployed and credit card)/n(Credit card)
=28/(18+28)
=0.608695652
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