Question

Selecting Condiments A box of condiments has ten small packages, in which three are ketchup, three are mustard, and four are relish. A sample of three packages is randomly selected (without replacement) from the box.

Suppose that you win $25 for each package of ketchup chosen and lose $15 otherwise. Let y denote the total winnings.
(a) Find the probability distribution for y.
(b) Verify that this distribution satisfies the axioms of a probability distribution.
(c) Calculate the expected loss.

Answer 1

(a)

Thus, probability distribution of Y is

Y=y	-45	-5	35	75
P(Y=y)	0.2916667	0.525	0.175	0.008333333

(b)

In the above probability distribution,

i) all the probabilities are larger than 0.

ii) Sum of all probabilities = 0.2916667 + 0.525+0.175+0.0083333 = 1

Hence, the axioms of probability are satisfied.

(c)

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