Question

Math 146 Probability Quiz A local espresso stand surveyed 50 of its customers on whether they preferred biscotti or muffins to eat, and then whether they preferred to drink lattes, mochas, cappuccinos or tea. The results are summarized below: latte: mocha: 13 cappuccino: tea: 0. biscotti: muffin: 10 1. What is the probability that a respondent, chosen at random, selected muffins on question 1? (Remember there are only 50 customers in the survey, not 100] 2. What is the probability that a respondent selected mocha on question 2? 3. What is the probability that a respondent selected muffins on question I and mocha on question 2? 4. What is the probability that a respondent selected muffins on question 1 or mocha on question 2? [Answer by using the Addition Rule -show work carefully]. 5. What is the probability that a respondent did not select mocha on question 2? [Answer by using the idea of a complement - show work carefully]. 6. What is the probability that if three respondents are selected at random, without replacement, all three chose mocha on question 2?

Answer 1

(1) required probability(respondent is muffin)=23/50=0.46

(2) required probability(mocha)=21/50=0.42

(3) required probability(muffin and mocha)=8/50=0.16

(4) required probability(muffin or mocha)= probability(muffin)+probability(mocha)- probability(muffin and mocha)=

=0.46+0.42-0.16=0.72

(5)P(didnot selected from mocha)=1-P(selected from mocha)=1-0.42=0.58

(6) required probability=(21/50)*(20/49)*(19/48)=0.0679

(7)required probability=(21/50)*(21/50)*(21/50)=0.0741

following information has been generated for answering the above question

frequency
	latte	mocha	cappuccino	tea	total
biscotti	10	13	0	4	27
muffin	7	8	5	3	23
total	17	21	5	7	50
probability
	latte	mocha	cappuccino	tea	total
biscotti	0.2	0.26	0	0.08	0.54
muffin	0.14	0.16	0.1	0.06	0.46
total	0.34	0.42	0.1	0.14	1