Please note that each of these questions requires answers in complete English se

Question

Please note that each of these questions requires answers in complete English sentences, and the last one requires explanations. You should show your work where appropriate ie. where is work to be shown) rather than just state final answers. As always, your work must be submitted via Sakai, and will not be accepted in any other form. There are no exceptions? ____ If you roll a fair die 1000 times, what is the expected number of times you will get a 5 (in the mathematical sense of expected)? If you roll a pair of fair dice l00 times, what is the expected number of times the sum will equal 11?

Explanation / Answer

In 1 dice , p = P(X =5) = 1/6   

hence

E(Y) = np = 1000/6 = 167 ,where Y is total number of dice to be showing 5.

b) P(X1 +X2 = 11) = 2/36 = 1/18 {6+5 ,5+6 } out of 6*6 =36 times

so required number = 100/18 = 5.5555

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