**** Gambling Dice Machine probability ****
A gambling machine:
A possiblity table of the possiblity of each side of a dice, from 1 to 6:
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|side | 1, 2, 3, 4, 5, 6 |
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|possiblity | 0.1, 0.2, 0.2,0.15,0.2,0.15 | (total possiblity of one)
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There are four dices on the screen.
__ __ __ __
|__| |__| |__| |__|
Each prize draw will roll the dices to show 4 random numbers based on
the probability provided in the table.
The award prize is the "sum" of all the numbers appeared in the 4 slots.
E.g. 3351 will have a prize of 3+3+5+1=12. So the prize is in the range
of 4 to 24.
Q1: What is the "average" prize for this gambling machine?
Q2: Generalize the question: n numbers, w_1, w_2, w_3 .... w_n, and
their corresponding possiblities: p_1, p_2, p_3 .... p_n. With
replacement, 4 boxes, each box filled with one number, what is the
average sum of these four numbers?
.
.
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