Four students go to get dinner at the SU and they each order

Four students go to get dinner at the SU and they each order a different dish. The third one orders Mac & Cheese. Unfortunately, things are so busy that the server randomly hands them each a dish. Compute the probability that the third person actually gets Mac & Cheese Compute the conditional probability that the third person gets Mac & Cheese given that the first person does not get the meal s/he ordered. Are the events \"the third person gets Mac k Cheese\" and \"the first person gets the wrong meal\" independent? Explain!

Solution

(a)

The sample space will contain a total of 4! arrangements since 4 dishes were ordered. The favourable case will contain 3! arrangements, since in this case the third person gets Mac and Cheese but the rest of 3 can have any arrangement of food.

Thus the probability will be 3!/4! = 1/4 = 0.25

(b)

The sample space will now contain the case when first person gets wrong meal. Thus sample space will have 3*3! arrangements.

Favourable cases will be when the third person gets Mac and Cheese but the first person doesnot get whatever he has ordered. Number of case will be 4.

Thus the probability for this part will be 4/3*3! = 0.22

(c)

If the events are independent then the conditional probability we have calculated above will be equal to the probability calculated in part a. But since they are not equal, the given events are not independent.