Question

Single Roll When we take the mean of the 25 successful rolls we get 8. We will assume that on a successful roll, the player earns 8 points. 25 P(success)= 36 11 P(failure)= 36 Value(success) = 8 Value(failure) 0 What is the expected value for a single roll? (Round to four decimal places) Two Rolls If we chose to pass the dice, then we would bank those points. If we chose to keep rolling, then in order to be successful we would need to roll no 1's twice. However, we would expect to get twice as many points IF we were to roll successfully. This would give us: 25 P(success)= 2 25 P(failure) 1- 36
Value(success) = 16 Value(failure) = 0 (Round to four decimal places) What is the expected value for rolling twice? More Rolls As you can see, if we chose to roll even more times, then we could calculate the probabilities and values in a similar way. If we were to roll n times, then we have: 25 P(success) = 36 25 P(failure) 1 36 Value(success) 8 - n Value(failure) = 0 What would the expected value be for: (Round to four decimal places) Three rolls? (Round to four decimal places) Four rolls?
(Round to four decimal places) Five rolls? Strategy Having looked at the five different strategies, which would you choose? ORoll once before passing ORoll twice before passing ORoll three times before passing ORoll four times before passing ORoll five times before passing Why would you choose this strategy?

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