document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200520>Question 1200520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Out of 1000 managers, 72% say they use social media to screen applications. Out of 5 applications, what is the probability that exactly 3 of the managers use social media to screen\r<BR>\n" );
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document.write( "What is the probability that non will use social media\r<BR>\n" );
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document.write( "What is the probability that all 5 will use social media </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848076 by </B><A HREF=/tutors/aboutme.mpl?userid=GingerAle><B>GingerAle(43)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=GingerAle><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=848076\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Define the Probability of Success**\r<BR>\n" );
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document.write( "* **Probability of Success (p):** <BR>\n" );
document.write( "    * The probability that a randomly selected manager uses social media to screen applications.<BR>\n" );
document.write( "    * p = 72% = 0.72\r<BR>\n" );
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document.write( "**2. Define the Probability of Failure (q)**\r<BR>\n" );
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document.write( "* **Probability of Failure (q):** <BR>\n" );
document.write( "    * The probability that a randomly selected manager does *not* use social media to screen applications.<BR>\n" );
document.write( "    * q = 1 - p = 1 - 0.72 = 0.28\r<BR>\n" );
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document.write( "**3. Use the Binomial Probability Formula**\r<BR>\n" );
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document.write( "* The probability of exactly k successes in n independent trials, where the probability of success in each trial is p, is given by the binomial probability formula:\r<BR>\n" );
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document.write( "   P(X = k) = (nCk) * p^k * q^(n-k) \r<BR>\n" );
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document.write( "   where:<BR>\n" );
document.write( "      * nCk = n! / (k! * (n-k)!) is the binomial coefficient \r<BR>\n" );
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document.write( "**a) Probability that exactly 3 of the 5 managers use social media:**\r<BR>\n" );
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document.write( "* n = 5 (number of trials)<BR>\n" );
document.write( "* k = 3 (number of successes)<BR>\n" );
document.write( "* p = 0.72 <BR>\n" );
document.write( "* q = 0.28\r<BR>\n" );
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document.write( "* P(X = 3) = (5C3) * (0.72)^3 * (0.28)^(5-3) <BR>\n" );
document.write( "           = (5! / (3! * 2!)) * (0.72)^3 * (0.28)²<BR>\n" );
document.write( "           = 10 * 0.373248 * 0.0784<BR>\n" );
document.write( "           = 0.2916\r<BR>\n" );
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document.write( "**Therefore, the probability that exactly 3 of the 5 managers use social media to screen applications is approximately 0.2916.**\r<BR>\n" );
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document.write( "**b) Probability that none of the 5 managers use social media:**\r<BR>\n" );
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document.write( "* n = 5<BR>\n" );
document.write( "* k = 0 (no successes)\r<BR>\n" );
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document.write( "* P(X = 0) = (5C0) * (0.72)^0 * (0.28)^(5-0) <BR>\n" );
document.write( "           = 1 * 1 * (0.28)^5<BR>\n" );
document.write( "           = 0.0014\r<BR>\n" );
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document.write( "**Therefore, the probability that none of the 5 managers use social media to screen applications is approximately 0.0014.**\r<BR>\n" );
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document.write( "**c) Probability that all 5 managers use social media:**\r<BR>\n" );
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document.write( "* n = 5<BR>\n" );
document.write( "* k = 5 (all successes)\r<BR>\n" );
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document.write( "* P(X = 5) = (5C5) * (0.72)^5 * (0.28)^(5-5) <BR>\n" );
document.write( "           = 1 * (0.72)^5 * 1<BR>\n" );
document.write( "           = 0.1935\r<BR>\n" );
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document.write( "**Therefore, the probability that all 5 managers use social media to screen applications is approximately 0.1935.**<BR>\n" );
document.write( " </SPAN>\n" );
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