Question

# Problem 4)A simplified version of the dice game 10,000 is played using 5 dice. The player...

Problem 4)A simplified version of the dice game 10,000 is played using 5 dice. The player rolls the 5 six-sided dice, each 1 that is rolled, the player achieves a score of 100.

A) How many possible ways are there to roll i l's over these 5 dice? (Hint: use combinations)

B) The probability of any one dice rolling to a value of 1 is 1/5 (since each dice has six sides). Use the binomial probability distribution. Calculate the probability of rolling

exactly i l's(i.e, calculate Pr(x=1) for each i)

C) The value of rolling i l's is i.100 since each 1 is worth 100. Assuming the player starts initially with 0 points and that all rolls not containing a 1 give no points. draw a probability tree representing the 6 possible monetary outcomes of this game.

D) Using the assumptions in part c, Calculate the expectation of this game.

E) If on the first roll, your only one 1 (thus obtain a value of 1000, should you roll again to attempt to get a better score.

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