From an urn (hat contains five red. five white, and five blue chips, we draw two

Question

From an urn (hat contains five red. five white, and five blue chips, we draw two chips at random without replacement. For each blue chip we win $1, for each white chip we win S2. but for each red chip wrc lose S3. If X represents the amount that wc either win or lose, what arc the possible values of X? Find the probability mass function of X. In a lottery every week. 2,000,000 tickets arc sold. If 4000 of these tickets pay off $30 each. 500 pay off $800 each, one ticket pays off $ 1, 200,000, and no ticket pays off more than one prize, what is the expected value of the winning amount fora player with a single ticket?

Explanation / Answer

Answers)

Problem 3. An urn has five red, five white and five blue chips. Two chips are selected at random without replacement.

So, the two chips can be selected as follows:

If X represents the amount that we either win or lose

The set of possible values of X is = { -6 , -2 , -1 , 2 , 3 , 4 }

Therefore, the probability mass function of X is given as:

Problem 4]  Suppose consider that 2000000 tickets are sold for $1 each.

Let X - The amount that one lottery ticket fetches

Then the expected value for the winning amount will be

E(X) = 30* (4000 / 2000000) + 800* (500 / 2000000) + 1200000 * (1/2000000) = 0.86

Therefore, the expectation of the net amount is E(X) - Cost of 1 lottery ticket = 0.86 - 1 = - 0.14

This indicates that for a player with a single ticket the expected value of the winning amount will be = -0.14

                                                                                                                                                              = $ 0.14 (Loss)

Red & White -3 + 2 = -1 (5/15) * (5/14) Red & Blue -3+1 = -2 (5/15) * (5/14) Red & Red -3 + -3 = -6 (5/15) * (4/14) White & Red 2 + -3 = -1 (5/15) * (5/14) White & Blue 2 + 1 = 3 (5/15) * (5/14) White & White 2 + 2 = 4 (5/15) * (4/14) Blue & Red 1 + -3 = -2 (5/15) * (5/14) Blue & White 1 + 2 = 3 (5/15) * (5/14) Blue & Blue 1 + 1 = 2 (5/15) * (4/14)

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