document.write( "Question 1195406: The probability that an athlete will not win any of the three races is 1/4. If the athlete runs in all the races, what is the probability that the athlete will win ( i) only the second race (ii) all the three races (iii) only two of the races \n" ); document.write( "

Algebra.Com's Answer #827899 by ikleyn(52782) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The probability that an athlete will not win any of the three races is 1/4.
\n" ); document.write( "If the athlete runs in all the races, what is the probability
\n" ); document.write( "that the athlete will win
\n" ); document.write( "(a) only the second race
\n" ); document.write( "(b) all the three races
\n" ); document.write( "(c) only two of the races
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            From the context, the probability for the athlete to win any of the three
\n" ); document.write( "            races is 3/4, as a complement to the given probability not to win of 1/4.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            Now it is easy to answer all questions, one after the other.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "(a)  P = P(lose,win,lose) =  = .    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  P = P(win,win,win) =  = .             ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(c)  P(win only 2 of 3 races) = use the formula of binomial distribution \r\n" );
document.write( "                                for 3 trials, 2 success and individual probability of success p = 3/4\r\n" );
document.write( "\r\n" );
document.write( "     = P(n=3, k=2, p=3/4) =  =  =  = .      ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Incidentally,  (b)  and  (c)  have equal probabilities.\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" );