document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001201>Question 1001201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question from Binomial Probability<BR>\n" );
document.write( "If three coins are tossed, find the probability of each number of heads.<BR>\n" );
document.write( "4) 3<BR>\n" );
document.write( "5) 1 or 2 <BR>\n" );
document.write( "6) at least 1\r<BR>\n" );
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document.write( "According to the book, For number 5 the answer is 3/4.<BR>\n" );
document.write( "would like to see solutions shown for all three. Thanks.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618443 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The binomial probability formula is<BR>\n" );
document.write( "P(k successes in n trials) = nCk * p^k * q^(n-k) where<BR>\n" );
document.write( "n = number of trials<BR>\n" );
document.write( "k = number of successes<BR>\n" );
document.write( "n-k = number of failures<BR>\n" );
document.write( "p = probability of success in one trial<BR>\n" );
document.write( "q = 1 – p = probability of failure in one trial<BR>\n" );
document.write( "nCk = combination of n trials taken k at a time<BR>\n" );
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document.write( "for our problem<BR>\n" );
document.write( "n = 3<BR>\n" );
document.write( "p = 0.50<BR>\n" );
document.write( "q = 0.50<BR>\n" );
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document.write( "4) 3 successes<BR>\n" );
document.write( "P(3 successes in 3 trials)= 3C3 * (0.50)^3 * (0.50)^(3-3) =<BR>\n" );
document.write( "(3! / (3! * (3-3)!) * (0.125) * 1 =<BR>\n" );
document.write( "0.125<BR>\n" );
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document.write( "5) first calculate<BR>\n" );
document.write( "P(0 successes in 3 trials) = 3C0 * (0.50)^0 * (0.50)^(3-0) =<BR>\n" );
document.write( "(3! / (0! * (3-0)!) * 1 * (0.125) =<BR>\n" );
document.write( "0.125<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "P(1 or 2 successes in 3 trials) = 1 - (P(3 successes in 3 trials) + P(0 successes in 3 trials)) =<BR>\n" );
document.write( "1 - (0.125 + 0.125) = 0.75 = 3/4<BR>\n" );
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document.write( "6) note that<BR>\n" );
document.write( "P(at least 1 success in 3 trials) = 1 - P(0 successes in 3 trials) =<BR>\n" );
document.write( "1 - 0.125 = 0.875<BR>\n" );
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