document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191591>Question 1191591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MAT 145: Topics In Contemporary Math<BR>\n" );
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document.write( "        More Probability\r<BR>\n" );
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document.write( "1) In a recent survey of 200 people, 120 identified themselves as male. Of the 120 males, 60% considered themselves heterosexual. Of the non-male identifiers, 35% considered themselves heterosexual. Let M be the event that a person identifies as male and H be the event that a person considers themselves heterosexual. Use this information to find each of the following.\r<BR>\n" );
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document.write( "𝑃(𝑀 𝑎𝑛𝑑 𝐻)        𝑃(𝑀 𝑎𝑛𝑑 𝐻^𝑐)\r<BR>\n" );
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document.write( "𝑃(𝑀𝑐𝑎𝑛𝑑 𝐻)        𝑃(𝑀^𝑐 𝑎𝑛𝑑 𝐻^𝑐)\r<BR>\n" );
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document.write( "𝑃(𝐻)               𝑃(𝐻^c)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849112 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=849112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate those probabilities:\r<BR>\n" );
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document.write( "1. **Calculate the number of people in each category:**\r<BR>\n" );
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document.write( "* **Males (M):** 120<BR>\n" );
document.write( "* **Non-males (Mᶜ):** 200 - 120 = 80<BR>\n" );
document.write( "* **Heterosexual males (M ∩ H):** 120 * 0.60 = 72<BR>\n" );
document.write( "* **Non-heterosexual males (M ∩ Hᶜ):** 120 - 72 = 48<BR>\n" );
document.write( "* **Heterosexual non-males (Mᶜ ∩ H):** 80 * 0.35 = 28<BR>\n" );
document.write( "* **Non-heterosexual non-males (Mᶜ ∩ Hᶜ):** 80 - 28 = 52<BR>\n" );
document.write( "* **Total heterosexual (H):** 72 + 28 = 100<BR>\n" );
document.write( "* **Total non-heterosexual (Hᶜ):** 48 + 52 = 100\r<BR>\n" );
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document.write( "2. **Calculate the probabilities:**\r<BR>\n" );
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document.write( "* **P(M and H):** (Number of heterosexual males) / (Total people) = 72 / 200 = 0.36<BR>\n" );
document.write( "* **P(M and Hᶜ):** (Number of non-heterosexual males) / (Total people) = 48 / 200 = 0.24<BR>\n" );
document.write( "* **P(Mᶜ and H):** (Number of heterosexual non-males) / (Total people) = 28 / 200 = 0.14<BR>\n" );
document.write( "* **P(Mᶜ and Hᶜ):** (Number of non-heterosexual non-males) / (Total people) = 52 / 200 = 0.26<BR>\n" );
document.write( "* **P(H):** (Total number of heterosexual people) / (Total people) = 100 / 200 = 0.50<BR>\n" );
document.write( "* **P(Hᶜ):** (Total number of non-heterosexual people) / (Total people) = 100 / 200 = 0.50<BR>\n" );
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