document.write( "Question 1198328: You are given an unfair coin with probability of obtaining a head equal to
\n" ); document.write( "1/3, 000, 000, 000. You toss this coin 6,000,000,000 times. Let A be the
\n" ); document.write( "event that you get “tails for all the tosses”. Let B be the event that you get
\n" ); document.write( "“heads for all the tosses”.
\n" ); document.write( "i) Approximate P (A).
\n" ); document.write( "ii) Approximate P (A ∪ B) \n" ); document.write( "

Algebra.Com's Answer #831935 by ikleyn(52847) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "You are given an unfair coin with probability of obtaining a head equal to 1/3, 000,000,000.
\n" ); document.write( "You toss this coin 6,000,000,000 times. Let A be the event that you get “tails for all the tosses”.
\n" ); document.write( "Let B be the event that you get “heads for all the tosses”.
\n" ); document.write( "i) Approximate P (A).
\n" ); document.write( "ii) Approximate P (A ∪ B)
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "For (i),  P(A) =  = ,\r\n" );
document.write( "\r\n" );
document.write( "          where n = 3,000,000,000.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "          From Calculus, it is well known fact that  \r\n" );
document.write( "\r\n" );
document.write( "               lim  =   as n --> oo.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "          So, P(A) =  =  = 0.1353  (approximately).    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For (ii), P(B) is extremely small and events A and B are mutially exclusive;\r\n" );
document.write( "\r\n" );
document.write( "          therefore, P(A U B) = P(A): P(B) contributes practically nothing.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );