document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201093>Question 1201093</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to the store’s historical records, 65% of its digital camera customers <BR>\n" );
document.write( "are male, 18% of its digital camera customers purchased the extended warranty, <BR>\n" );
document.write( "and 10% of its digital camera customers are female and purchased the extended <BR>\n" );
document.write( "warranty. <BR>\n" );
document.write( "(i) Determine the probability that a male digital camera customer will <BR>\n" );
document.write( "purchase the extended warranty. [4 Marks]<BR>\n" );
document.write( "(ii) Are female customers more likely to purchase the extended warranty? <BR>\n" );
document.write( "Justify your answers  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848093 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=848093\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly, let's analyze the probabilities related to digital camera customers and extended warranties.\r<BR>\n" );
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document.write( "**i) Probability of a male customer purchasing the extended warranty**\r<BR>\n" );
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document.write( "* **Let's define the events:**<BR>\n" );
document.write( "    * M: Event that a customer is male<BR>\n" );
document.write( "    * F: Event that a customer is female<BR>\n" );
document.write( "    * W: Event that a customer purchases the extended warranty\r<BR>\n" );
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document.write( "* **Given probabilities:**<BR>\n" );
document.write( "    * P(M) = 0.65 (Probability of a male customer)<BR>\n" );
document.write( "    * P(W) = 0.18 (Probability of purchasing the extended warranty)<BR>\n" );
document.write( "    * P(F ∩ W) = 0.10 (Probability of a female customer purchasing the extended warranty)\r<BR>\n" );
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document.write( "* **Find P(M ∩ W) (Probability of a male customer purchasing the extended warranty):**\r<BR>\n" );
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document.write( "    * We know:<BR>\n" );
document.write( "        * P(M ∪ F) = 1 (Since all customers are either male or female)<BR>\n" );
document.write( "        * P(W) = P(M ∩ W) + P(F ∩ W) \r<BR>\n" );
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document.write( "    * Therefore:<BR>\n" );
document.write( "        * P(M ∩ W) = P(W) - P(F ∩ W) <BR>\n" );
document.write( "        * P(M ∩ W) = 0.18 - 0.10 = 0.08\r<BR>\n" );
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document.write( "* **Calculate the conditional probability P(W | M):**\r<BR>\n" );
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document.write( "    * P(W | M) = P(M ∩ W) / P(M) = 0.08 / 0.65 ≈ 0.1231\r<BR>\n" );
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document.write( "**Therefore, the probability that a male digital camera customer will purchase the extended warranty is approximately 0.1231 or 12.31%.**\r<BR>\n" );
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document.write( "**ii) Are female customers more likely to purchase the extended warranty?**\r<BR>\n" );
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document.write( "* **Find the probability of a female customer purchasing the extended warranty:**\r<BR>\n" );
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document.write( "    * P(W | F) = P(F ∩ W) / P(F) <BR>\n" );
document.write( "    * P(F) = 1 - P(M) = 1 - 0.65 = 0.35 <BR>\n" );
document.write( "    * P(W | F) = 0.10 / 0.35 ≈ 0.2857\r<BR>\n" );
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document.write( "* **Compare the probabilities:**\r<BR>\n" );
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document.write( "    * P(W | M) ≈ 0.1231 <BR>\n" );
document.write( "    * P(W | F) ≈ 0.2857\r<BR>\n" );
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document.write( "* **Conclusion:**\r<BR>\n" );
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document.write( "    * Since P(W | F) > P(W | M), **female customers are more likely to purchase the extended warranty.**\r<BR>\n" );
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document.write( "I hope this helps! Let me know if you have any other questions.<BR>\n" );
document.write( " </SPAN>\n" );
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