Question

Jiapeng is going to a New Year’s celebration. He will bring two dishes to share with his friends but has not yet decided what to bring. He will bring one main dish and one dessert. For the main dish he will choose to bring dumplings or spring rolls. For the dessert he will choose rice cakes or egg tarts. Here is some additional information.

• Jiapeng will bring dumplings with probability 0.64.

• If Jiapeng brings dumplings, then the probability that he brings rice cakes is 0.72.

• If Jiapeng brings spring rolls, then the probability that he brings egg tarts is 0.25.

(a) What is the probability Jiapeng brings rice cakes to the New Year’s celebration?

(b) Assuming Jiapeng brings egg tarts to the party, what is the probability he brings spring rolls?

(c) Is Jiapeng’s choice of main dish independent of his choice of dessert? Justify your answer mathematically.

Answer 1

a) probability Jiapeng brings rice cakes to the New Year’s celebration=P(dumpling)*P(rice cake|dumpling)+P(spring rolls)*P(rice cake|spring rolls) =0.64*0.72+(1-0.64)*(1-0.25)=0.7308

b)

P(spring rolls |egg tarts)=P(spring roll)*P(egg tarts|spring roll)/P(egg tarts)=(1-0.64)*0.25/(1-0.7308)=0.334324

c)

as P(spring rolls |egg tarts) =0.334324 is not equal to probability of spring roll=1-0.64 =0.36.

hence Jiapeng’s choice of main dish is not independent of his choice of dessert