document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190311>Question 190311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A baseball player hits a homerun on the average of once every 12 times at bat. Use the idea of independent trials to answer the following questions.\r<BR>\n" );
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document.write( "    If he bats 5 times in a game, what is the probability he will hit exactly one home run? <BR>\n" );
document.write( "    If he comes to bat 5 times, what is the probability he will hit at least one home run? <BR>\n" );
document.write( "    If he comes to bat 5 times in a game, what is the expected value for the number of home runs he will hit? \r<BR>\n" );
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document.write( "thanks for your help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142834 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142834\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A baseball player hits a homerun on the average of once every 12 times at bat. Use the idea of independent trials to answer the following questions.<BR>\n" );
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document.write( "If he bats 5 times in a game, what is the probability he will hit exactly one home run? <BR>\n" );
document.write( "It's binomial with n=5, p = 1/12,  x = 1 <BR>\n" );
document.write( "If you use a TI calculator you get binompdf(5,12^-1,1) = 0.2942<BR>\n" );
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document.write( "If you do not have a TI: P(x=1) = 5C1(1/12)^1(11/12)^4 <BR>\n" );
document.write( "= 5*(1/12)(0.70607) = 0.2942<BR>\n" );
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document.write( "If he comes to bat 5 times, what is the probability he will hit at least one home run? <BR>\n" );
document.write( "P(at least one) = 1 - P(no home runs) = 1-binompdf(5,12^-1,0) = 0.3528<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "P(at least one) = 1-P(no home runs) = 1 - 5C0(1/12)^0(11/12)^5 <BR>\n" );
document.write( "= 1 - 1*1* = 1-0.6472 = 0.3528<BR>\n" );
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document.write( "If he comes to bat 5 times in a game, what is the expected value for the number of home runs he will hit? <BR>\n" );
document.write( "E(x) = np = 5(1/12) = 5/12<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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