document.write( "Question 681555: a group of 6 men and 8 women and 5 people are chosen at random,
\n" ); document.write( "find probability that:
\n" ); document.write( "a) There are exactly 3 men.
\n" ); document.write( "b)There are at most 2 woman.
\n" ); document.write( "c) There are more men than woman. \n" ); document.write( "
Algebra.Com's Answer #422690 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "a group of 6 men and 8 women and 5 people are chosen at random,
\n" ); document.write( "find probability that:
\n" ); document.write( "a) There are exactly 3 men.
\n" ); document.write( "b)There are at most 2 woman.
\n" ); document.write( "c) There are more men than woman.
\n" ); document.write( "
\r\n" );
document.write( "----------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "There are three ways to do binomial problems:\r\n" );
document.write( "\r\n" );
document.write( "1.  By a probability table\r\n" );
document.write( "2.  By using a TI-83 or 84 calculator\r\n" );
document.write( "3.  By formula\r\n" );
document.write( "\r\n" );
document.write( "You didn't specify which way, so I'll do it the easiest way,\r\n" );
document.write( "with a TI-83 or 84 calculator.  If your teacher doesn't allow the\r\n" );
document.write( "use of those calclators, then post again, stating which of the other\r\n" );
document.write( "two methods you are to use.\r\n" );
document.write( "\r\n" );
document.write( "-----------------\r\n" );
document.write( "\r\n" );
document.write( "When using the calculator, the trick is knowing whether to use\r\n" );
document.write( "binompdf or binomcdf.  The \"p\" is for a particular value of x,\r\n" );
document.write( "and the \"c\" is for the cumulative value from 0 up to the value of x.  \r\n" );
document.write( "\r\n" );
document.write( "n = number of trials = 5\r\n" );
document.write( "p = 6/14 = 3/7 is the probability of selecting 1 man in 1 trial\r\n" );
document.write( "p = 8/14 = 4/7 is the probability of selecting 1 woman in 1 trial\r\n" );
document.write( "x = number of men or the number of women depending on the problem\r\n" );
document.write( "

\n" ); document.write( "a) There are exactly 3 men.
\n" ); document.write( "
\r\n" );
document.write( "n = 5, p = 3/7, x = 3\r\n" );
document.write( "\r\n" );
document.write( "This is a particular value, 3 for x, so we use binompdf:\r\n" );
document.write( "\r\n" );
document.write( "Press 2nd, then VARS, then scroll down to binompdf( and press ENTER\r\n" );
document.write( "\r\n" );
document.write( "On the later models TI-84 you are asked for the trials, which is 5,\r\n" );
document.write( "p: which is 3/7, and the x value which is 3, then you scroll to paste and\r\n" );
document.write( "press ENTER, you'll see:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "binompdf(5,3/7,3\r\n" );
document.write( ")\r\n" );
document.write( "\r\n" );
document.write( "On older models and the TI-83 you type \"3/7,3)\"  so that you have the above.\r\n" );
document.write( "Then you press ENTER and read\r\n" );
document.write( "\r\n" );
document.write( ".2570357589\r\n" );
document.write( "

\n" ); document.write( "b) There are at most 2 women.
\n" ); document.write( "
\r\n" );
document.write( "n = 5, p = 4/7, x = 2\r\n" );
document.write( "\r\n" );
document.write( "This is a cumulative value, for 0, 1, or 2 women, so we use binomcdf\r\n" );
document.write( "\r\n" );
document.write( "We have a maximum value of 2 for x:\r\n" );
document.write( "\r\n" );
document.write( "Press 2nd, then VARS, then scroll down to binomcdf( and press ENTER\r\n" );
document.write( "\r\n" );
document.write( "On the later models TI-84 you are asked for the trials, which is 5,\r\n" );
document.write( "p: which is 4/7, and the x value which is 2, then you scroll to paste and\r\n" );
document.write( "press ENTER, you'll see:\r\n" );
document.write( "\r\n" );
document.write( "binomcdf(5,4/7,2\r\n" );
document.write( ")\r\n" );
document.write( "\r\n" );
document.write( "On older models and the TI-83 you type \"4/7,2)\"  so that you have the above.\r\n" );
document.write( "Then you press ENTER and read\r\n" );
document.write( "\r\n" );
document.write( ".3678824299\r\n" );
document.write( "

\n" ); document.write( "c) There are more men than woman.
\n" ); document.write( "
\r\n" );
document.write( "That means there are 3 men and 2 women, 4 men and 1 woman, \r\n" );
document.write( "or 5 men and 0 women:\r\n" );
document.write( "\r\n" );
document.write( "This is the same as problem b, which is also 0, 1, or 2 women. So\r\n" );
document.write( "the answer is the same.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );