document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167569>Question 1167569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following data for an imaginary superhero universe:\r<BR>\n" );
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document.write( " Flying 	 Telepathy 	 Super Strength <BR>\n" );
document.write( "Female	98	58	49<BR>\n" );
document.write( "Male	96	80	56<BR>\n" );
document.write( "Distribution of Super Power by Gender<BR>\n" );
document.write( "What is the empirical probability that a randomly selected female superhero will have Super Strength?\r<BR>\n" );
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document.write( "Answer in decimal form.  Round to 3 decimal places as needed </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852325 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</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=852325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ```python?code_reference&code_event_index=2<BR>\n" );
document.write( "# Data provided in the table for Female superheroes<BR>\n" );
document.write( "female_flying = 98<BR>\n" );
document.write( "female_telepathy = 58<BR>\n" );
document.write( "female_super_strength = 49\r<BR>\n" );
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document.write( "# 1. Calculate the Total Number of Female Superheroes<BR>\n" );
document.write( "total_female = female_flying + female_telepathy + female_super_strength\r<BR>\n" );
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document.write( "# 2. Identify the Number of Female Superheroes with Super Strength<BR>\n" );
document.write( "female_super_strength_count = female_super_strength\r<BR>\n" );
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document.write( "# 3. Calculate the Empirical Conditional Probability: P(Super Strength | Female)<BR>\n" );
document.write( "probability = female_super_strength_count / total_female\r<BR>\n" );
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document.write( "# Print results<BR>\n" );
document.write( "print(f\"Total Female Superheroes: {total_female}\")<BR>\n" );
document.write( "print(f\"Female Super Strength Count: {female_super_strength_count}\")<BR>\n" );
document.write( "print(f\"Probability (decimal): {probability}\")<BR>\n" );
document.write( "print(f\"Probability (rounded to 3 decimal places): {probability:.3f}\")\r<BR>\n" );
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document.write( "```\r<BR>\n" );
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document.write( "```text?code_stdout&code_event_index=2<BR>\n" );
document.write( "Total Female Superheroes: 205<BR>\n" );
document.write( "Female Super Strength Count: 49<BR>\n" );
document.write( "Probability (decimal): 0.23902439024390243<BR>\n" );
document.write( "Probability (rounded to 3 decimal places): 0.239\r<BR>\n" );
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document.write( "```\r<BR>\n" );
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document.write( "The empirical probability that a randomly selected **female** superhero will have **Super Strength** is **0.239**.\r<BR>\n" );
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document.write( "This is a **conditional probability** calculated as the ratio of female superheroes with Super Strength to the total number of female superheroes.\r<BR>\n" );
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document.write( "### Calculation Steps\r<BR>\n" );
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document.write( "1.  **Total Number of Female Superheroes (Sample Space):**<BR>\n" );
document.write( "    $$\text{Total Female} = 98 (\text{Flying}) + 58 (\text{Telepathy}) + 49 (\text{Super Strength}) = 205$$\r<BR>\n" );
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document.write( "2.  **Number of Female Superheroes with Super Strength (Event Count):**<BR>\n" );
document.write( "    $$\text{Female Super Strength} = 49$$\r<BR>\n" );
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document.write( "3.  **Empirical Probability:**<BR>\n" );
document.write( "    $$P(\text{Super Strength} | \text{Female}) = \frac{\text{Female Super Strength}}{\text{Total Female}} = \frac{49}{205} \approx 0.23902...$$\r<BR>\n" );
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document.write( "Rounding to 3 decimal places gives **0.239**. </SPAN>\n" );
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