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1. Ben Plowin, from Iowa, draws a card at random from a standard deck. What is the probability that he will draw a seven?

   
   

   There are 52 cards in a deck, four of which are 7's, one for each suit: Spades, Hearts, Diamonds and Clubs.

2. Given that Ben has drawn is a seven, what is the probability that it is a club?

   
   

   There are four suits for any given card face value, so the probability that it is a Club is 1/4.

   Marge N. Overra has been observing visitors to Atlantic City and their choice of one armed bandit. She has compiled the following table of results on age and the choice of nickel versus dollar slots.
   

   		Age
   		Over 60	Under 60
   Cost of Play	Nickel slot machine	.4	.2
   	Dollar slot machine	.1	.3

3. Are the events 'Age' and 'Cost of Play' independent? Select any of the following options that apply:

   Independent
   Mutually exclusive
   Dependent
   

   Add another row and another column so that you can fill in the marginal probabilities.  The test for statistical independence is whether the product of the marginals equals the joint probability.  In this case P(nickel) = .6 and P(Over 60) = .5, so P(nickel)*P(over 60) = .30.  But intersection is P(nickel and over 60) = .40, so the events "age" and "cost of play" are not equal.

4. You have three coins.  You toss them all on the table at once.  What is the probability of two or more 'heads'?
   
   
   You can do this using the binomial probability distribution, if you already know it, or you can enumerate the sample space and calculate the relative frequency of two or more heads.  The list of all possible outcomes is: HTT, HHT, HHH, THH, TTH, TTT, HTH, and THT.  There are a total of 8 outcomes, of which 4 include two or more heads. The answer is 1/2.
   
5. In the 'three coin toss' of question 4, your aunt, E. Lucy Dayte, pays you $2 for each head that is showing and you pay her $1 for each tail that is showing.  What are your expected earnings from any toss of the three coins.
   $
   

   Outcome	Probability	Payoff	Probability*Payoff
   3 Heads	1/8	6	6/8
   2 Heads	3/8	3	9/8
   1 Head	3/8	0	0
   0 Heads	1/8	-3	-3/8
   			Column sum = 1.5

   The expected value of the game is $1.50.
   

6. In the three coin toss problem, what is the variance of your earnings?
   
   

   Outcome	Probability	Payoff-E(payoff)	(Payoff-E(Payoff)2	Col 2 x Col 3
   3 Heads	1/8	4.5	20.25	2.53
   2 Heads	3/8	1.5	2.25	.844
   1 Head	3/8	-1.5	2.25	.844
   0 Heads	1/8	-4.5	20.25	2.53
   			Sum of last column =	6.75