Only need Exercise 5 answered! tossing is HHTTHHHHTHTH, then there are 4 runs of

Question

Only need Exercise 5 answered!

tossing is HHTTHHHHTHTH, then there are 4 runs of heads. Note that it's po contain only one head. If P(heads) p, find the expected number of runs Exercise 5 Roll a pair of dice. Find the expected value of the first die if the sum is 4. Exercise 6 A student working on a problem has three available methods Method A takes 5 hours but doesn't solve the problem. Method B takes 2 hours and also leads nowhere. Method C leads to a solution after 4 hours of work. If the student has no reason to favor one untried method over another but

Explanation / Answer

Exercise 5

First die cannot have any other number when the sum of two dice is 4.

P(1 on die 1) = Favorable outcomes/Total number of outcomes = 6/36 = 0.167

p(2 on die 1) = 0.167

P(3 on die 1) 0.167

So expected value on die 1 = 1 * 0.167 + 2 * 0.167 + 3 * 0.167 = 0.167 + 0.334 + 0.501 = 1.002 is the answer

First Die Second Die Sum 1 3 4 2 2 4 3 1 4

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