Question 1198328
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You are given an unfair coin with probability of obtaining a head equal to 1/3, 000,000,000. 
You toss this coin 6,000,000,000 times. Let A be the event that you get “tails for all the tosses”. 
Let B be the event that you get “heads for all the tosses”.
i) Approximate P (A).
ii) Approximate P (A ∪ B)
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For (i),  P(A) = {{{(1-1/3000000000)^6000000000}}} = {{{(1-1/n)^(2n)}}},

          where n = 3,000,000,000.


          From Calculus, it is well known fact that  

               lim {{{(1-1/n)^(2n)}}} = {{{e^(-2)}}}  as n --> oo.


          So, P(A) = {{{e^(-2)}}} = {{{2.71828^(-2)}}} = 0.1353  (approximately).    <U>ANSWER</U>



For (ii), P(B) is extremely small and events A and B are mutially exclusive;

          therefore, P(A U B) = P(A): P(B) contributes practically nothing.
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Solved.