Answer in Statistics and Probability for jaya #126784
Let “V” be the event of customers ordering vegetarian meals and “S” be the event of customers being students.
“P(V)=0.35, P(S)=0.5, P(V|S)=0.25”
I. The probability that a randomly chosen customer both is a student and orders a
vegetarian meal
“P(Vcap S)=P(S)P(V|S)=0.5cdot0.25=0.125”
II. If a randomly chosen customer orders a vegetarian meal, what is the probability that the customer is a student
“P(S|V)={P(Vcap S)over P(V)}={0.125over 0.35}={5over 14}approx0.357”
III. What is the probability that a randomly chosen customer both does not order a
vegetarian meal and is not a student?
From De Morgan’s Laws
“P(V^ccap S^c)=P(overline{Vcup S})”
Then
“P(V^ccap S^c)=P(overline{Vcup S})=1-P(Vcup S)=”
“=1-(P(V)+P(S)-P(Vcap S))=”
“=1-(0.35+0.5-0.125)=0.275”
IV. Are the events “customer orders a vegetarian meal” and “customer is a student”
independent?
“P(Vcap S)=0.125not=0.175=0.35cdot 0.5=P(V)P(S)”
Therefore the events “customer orders a vegetarian meal” and “customer is a student” are not independent.
V. Are the events “customer orders a vegetarian meal” and “customer is a student”
mutually exclusive?
“P(Vcap S)=0.125not=0”
Therefore the events “customer orders a vegetarian meal” and “customer is a student” are not mutually exclusive.
