Answer to Question #208976 in Statistics and Probability for mimi

Question #208976

A takeaway pizza shop conducted analysis of the takeaway meals ordered, and found that 40%

of orders were for a meat pizza with a drink, 20% for a vegetarian pizza with a drink, 10% for a

meat pizza without a drink, and 30% for a vegetarian pizza without a drink. If a takeaway order is

randomly selected, find the probability that it is for:

(a) A meat pizza without a drink. (2)

(b) An order with a drink. (2)

(c) A meat pizza. (2)

(d) A meat pizza or an order with a drink. (3)

(e) A meat pizza, if the order included a drink. (2)

(f) An order with a drink, if a vegetarian pizza was ordered.


1
Expert's answer
2021-06-23T08:30:09-0400

(a)


P(MD)=0.1P(M\cap D')=0.1

(b)


P(D)=P(MD)+P(VD)P(D)=P(M\cap D)+P(V\cap D)




=0.4+0.2=0.6=0.4+0.2=0.6



(c)


P(M)=P(MD)+P(MD)P(M)=P(M\cap D)+P(M\cap D')

=0.4+0.1=0.5=0.4+0.1=0.5

(d)


P(MD)=1P(VD)P(M\cup D)=1-P(V\cap D')

=10.3=0.7=1-0.3=0.7

Or

P(MD)=P(M)+P(VD)P(M\cup D)=P(M)+P(V\cap D)

=0.5+0.2=0.7=0.5+0.2=0.7

(e)


P(MD)=P(MD)P(D)=0.40.6=23P(M|D)=\dfrac{P(M\cap D)}{P(D)}=\dfrac{0.4}{0.6}=\dfrac{2}{3}

(f)


P(V)=P(VD)+P(VD)P(V)=P(V\cap D)+P(V\cap D')

=0.2+0.3=0.5=0.2+0.3=0.5


P(DV)=P(VD)P(V)=0.20.5=0.4P(D|V)=\dfrac{P(V\cap D)}{P(V)}=\dfrac{0.2}{0.5}=0.4


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