document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167570>Question 1167570</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	89	46	12<BR>\n" );
document.write( "Male	35	38	82<BR>\n" );
document.write( "Distribution of Super Power by Gender<BR>\n" );
document.write( "What is the empirical probability that a randomly selected 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 #852324 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=852324\">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<BR>\n" );
document.write( "data = {<BR>\n" );
document.write( "    'Female': {'Flying': 89, 'Telepathy': 46, 'Super Strength': 12},<BR>\n" );
document.write( "    'Male': {'Flying': 35, 'Telepathy': 38, 'Super Strength': 82}<BR>\n" );
document.write( "}\r<BR>\n" );
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document.write( "# 1. Calculate Total Superheroes<BR>\n" );
document.write( "total_female = sum(data['Female'].values())<BR>\n" );
document.write( "total_male = sum(data['Male'].values())<BR>\n" );
document.write( "total_superheroes = total_female + total_male\r<BR>\n" );
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document.write( "# 2. Calculate Total Superheroes with Super Strength<BR>\n" );
document.write( "total_super_strength = data['Female']['Super Strength'] + data['Male']['Super Strength']\r<BR>\n" );
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document.write( "# 3. Calculate Empirical Probability of Super Strength<BR>\n" );
document.write( "probability_super_strength = total_super_strength / total_superheroes\r<BR>\n" );
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document.write( "# Print results<BR>\n" );
document.write( "print(f\"Total Superheroes: {total_superheroes}\")<BR>\n" );
document.write( "print(f\"Total Super Strength Superheroes: {total_super_strength}\")<BR>\n" );
document.write( "print(f\"Probability of Super Strength (decimal): {probability_super_strength}\")<BR>\n" );
document.write( "print(f\"Probability of Super Strength (rounded to 3 decimal places): {probability_super_strength:.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 Superheroes: 302<BR>\n" );
document.write( "Total Super Strength Superheroes: 94<BR>\n" );
document.write( "Probability of Super Strength (decimal): 0.31125827814569534<BR>\n" );
document.write( "Probability of Super Strength (rounded to 3 decimal places): 0.311\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 superhero will have **super strength** is **0.311**.\r<BR>\n" );
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document.write( "This is calculated as the ratio of the total number of superheroes with super strength to the total number of superheroes.\r<BR>\n" );
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document.write( "### Calculation Steps\r<BR>\n" );
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document.write( "1.  **Total Super Strength Superheroes:**<BR>\n" );
document.write( "    $$\text{Total Super Strength} = \text{Female} + \text{Male} = 12 + 82 = 94$$\r<BR>\n" );
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document.write( "2.  **Total Superheroes (Sample Size):**<BR>\n" );
document.write( "    $$\begin{aligned} \text{Total Superheroes} &= (\text{Female Total}) + (\text{Male Total}) \\ &= (89 + 46 + 12) + (35 + 38 + 82) \\ &= 147 + 155 \\ &= 302 \end{aligned}$$\r<BR>\n" );
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document.write( "3.  **Empirical Probability:**<BR>\n" );
document.write( "    $$P(\text{Super Strength}) = \frac{\text{Total Super Strength}}{\text{Total Superheroes}} = \frac{94}{302} \approx 0.311258...$$\r<BR>\n" );
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document.write( "Rounding to 3 decimal places gives **0.311**. </SPAN>\n" );
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