document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200375>Question 1200375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Raffle tickets numbered 1 through 30 are placed in a box. Tickets for a second raffle are<BR>\n" );
document.write( "numbered 21 through 48 and placed in a second box. One ticket is randomly drawn from each box.<BR>\n" );
document.write( "Find the probability the first ticket is greater than 10, and the second ticket is less than 40 or odd </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848081 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=848081\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly, let's find the probability.\r<BR>\n" );
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document.write( "**1. Probability of the first ticket being greater than 10:**\r<BR>\n" );
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document.write( "* There are 20 tickets numbered greater than 10 (from 11 to 30) out of a total of 30 tickets.<BR>\n" );
document.write( "* Probability of the first ticket being greater than 10: 20/30 = 2/3\r<BR>\n" );
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document.write( "**2. Probability of the second ticket being less than 40 or odd:**\r<BR>\n" );
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document.write( "* **Less than 40:** There are 19 tickets less than 40 (from 21 to 39) out of 28 total tickets.<BR>\n" );
document.write( "* **Odd numbers:** There are 14 odd numbers (21, 23, 25, ..., 47) out of 28 total tickets.<BR>\n" );
document.write( "* **Less than 40 and odd:** There are 10 numbers that are both less than 40 and odd (21, 23, 25, ..., 39).\r<BR>\n" );
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document.write( "* To find the probability of \"less than 40 or odd\", we use the formula:<BR>\n" );
document.write( "    * P(A or B) = P(A) + P(B) - P(A and B) <BR>\n" );
document.write( "    * where:<BR>\n" );
document.write( "        * P(A) = Probability of the ticket being less than 40 <BR>\n" );
document.write( "        * P(B) = Probability of the ticket being odd<BR>\n" );
document.write( "        * P(A and B) = Probability of the ticket being both less than 40 and odd\r<BR>\n" );
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document.write( "* P(less than 40 or odd) = (19/28) + (14/28) - (10/28) = 23/28\r<BR>\n" );
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document.write( "**3. Probability of both events happening:**\r<BR>\n" );
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document.write( "* Since the draws are independent, the probability of both events happening is the product of their individual probabilities.\r<BR>\n" );
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document.write( "* Probability = (Probability of first ticket > 10) * (Probability of second ticket < 40 or odd)<BR>\n" );
document.write( "* Probability = (2/3) * (23/28) <BR>\n" );
document.write( "* Probability = 23/42\r<BR>\n" );
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document.write( "**Therefore, the probability that the first ticket is greater than 10 and the second ticket is less than 40 or odd is 23/42.**<BR>\n" );
document.write( " </SPAN>\n" );
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