document.write( "Question 1199959: A coin is Twice as likely to turn up Head as Tails in a sequences of independent
\n" ); document.write( "tosses of the coin. What is the probability that the 3rd Head occurs on the 6th
\n" ); document.write( "tosses. \n" ); document.write( "

Algebra.Com's Answer #833958 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A coin is Twice as likely to turn up Head as Tails in a sequences of independent
\n" ); document.write( "tosses of the coin. What is the probability that the 3rd Head occurs on the 6th
\n" ); document.write( " $\"highlight%28cross%28tosses%29%29\"$ toss?
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "From the problem,  P(Head) = 2/3;  P(Tail) = 1/3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, the event that the 3rd Head occurs on the 6th toss is the intersection of two independent events, A and B.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Event A is that in the first 5 tosses the Head will occur exactly two times.\r\n" );
document.write( "\r\n" );
document.write( "    Event B is that the 6th toss will be Head.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Event A is the binomial with the number of trials n= 5, number of success trials k= 2\r\n" );
document.write( "and the probability of success (=Head) of 2/3;  so\r\n" );
document.write( "\r\n" );
document.write( "    P(A) =  =  = 0.164609.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For event B,  P(B) = P(Head) = 2/3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore,  P(A and B) = P(A)*P(B) =  = 0.109739  (rounded).    ANSWER\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" );