document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168310>Question 1168310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On average there are three babies born a day at the Hospital with hair on their backs.  Find the probability that in one day no babies are born with hair on their backs.\r<BR>\n" );
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document.write( "Round answer to 4 decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851582 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851582\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem can be solved using the Poisson distribution, which is used to model the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known average rate and independently of the time since the last event.\r<BR>\n" );
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document.write( "**1. Understand the Poisson Distribution**\r<BR>\n" );
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document.write( "* The Poisson distribution formula is: P(X = k) = (e^(-λ) * λ^k) / k!<BR>\n" );
document.write( "    * P(X = k) is the probability of k events occurring.<BR>\n" );
document.write( "    * λ (lambda) is the average number of events (in this case, babies born with hair on their backs).<BR>\n" );
document.write( "    * e is Euler's number (approximately 2.71828).<BR>\n" );
document.write( "    * k! is the factorial of k.\r<BR>\n" );
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document.write( "**2. Identify the Values**\r<BR>\n" );
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document.write( "* λ = 3 (average number of babies born with hair on their backs per day)<BR>\n" );
document.write( "* k = 0 (we want to find the probability of no babies born with hair on their backs)\r<BR>\n" );
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document.write( "**3. Apply the Poisson Formula**\r<BR>\n" );
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document.write( "* P(X = 0) = (e^(-3) * 3^0) / 0!<BR>\n" );
document.write( "* P(X = 0) = (e^(-3) * 1) / 1<BR>\n" );
document.write( "* P(X = 0) = e^(-3)\r<BR>\n" );
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document.write( "**4. Calculate the Probability**\r<BR>\n" );
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document.write( "* e^(-3) ≈ 0.049787\r<BR>\n" );
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document.write( "**5. Round to 4 Decimal Places**\r<BR>\n" );
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document.write( "* P(X = 0) ≈ 0.0498\r<BR>\n" );
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document.write( "**Therefore, the probability that no babies are born with hair on their backs in one day is approximately 0.0498.**<BR>\n" );
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