Question

Q1) Draw 4 chips one-by-one without replacement from an urn that contains 14 red and 6 black chips. Suppose you win $5 for each black chip drawn. Find your expected winnings.

Q2) Michael and Christine play a game where Michael selects a number from the set {1,2,3,4,....8}. He receives N dollars if the card selected is even; otherwise, Michael pays Christine two dollars. Determine the value of N if the game is to be fair.

Answer 1

Q1) As we are drawing 4 chips without replacement here. The number of black chips that are drawn from the urn probabilities are computed here as:

and so on.. .

The expected winnings now is computed here as:

= 0*P(X = 0) + 5*P(X = 1) + 2*5*P(X = 2) + 3*5*P(X = 3) + 4*5P(X = 4)

X	P(X = x)	Winnings
0	0.20660475	0
1	0.45077399	2.25386997
2	0.28173375	2.81733746
3	0.05779154	0.86687307
4	0.00309598	0.0619195
	1	6

The expected winnings now are computedhere as:

This is clearly obtained from the above table as:

Therefore $6 is the expected winning amount here.