Question

    2       3          4     5          6       7         8

6216 12674 18702 24978 18552 12678 6200

Table II
X	Frequency	Relative Freq.
2	6216	0.06216
3	12674	0.12674
4	18702	0.18702
5	24978	0.24978
6	18552	0.18552
7	12678	0.12678
8	6200	0.062

1. Use your table to calculate the total amount of money your group won. It is important to show your work on this exercise.

X*F

12432

38022

74808

124,890

111,312

88,746

49,600

                          

Total = $499,810

1. How much did your group win “on average”.
2. The law of large numbers tells us that “in the long run” the relative frequency of an event will tend towards its probability. Use your knowledge of probability to calculate the probability distribution for this gamble. How do your results compare to your previous tables?

3. Probability Distribution
   X	P (X)
   2
   3
   4
   5
   6
   7
   8

4. Use your table to compute the expected value of this gamble. Interpret the expected value in this context.

Answer 1

X	Frequency (F)	Relative Freq.	F*X
2	6216	0.06216	12432
3	12674	0.12674	38022
4	18702	0.18702	74808
5	24978	0.24978	124890
6	18552	0.18552	111312
7	12678	0.12678	88746
8	6200	0.062	49600
Total	100000		499810

Total = $499,810

a)

b) and c) The probability distribution for this gamble is

X	Relative Freq.= P(X)
2	0.06216
3	0.12674
4	0.18702
5	0.24978
6	0.18552
7	0.12678
8	0.062

The relative frequency of X is equivalent to the probability of X that is P(X).

d)

X	Relative Freq.= P(X)	X*P(X)
2	0.06216	0.12432
3	0.12674	0.38022
4	0.18702	0.74808
5	0.24978	1.2489
6	0.18552	1.11312
7	0.12678	0.88746
8	0.062	0.496
		4.9981

e) The mean of the game is 4.9981.