document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167571>Question 1167571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following data for an imaginary superhero universe:\r<BR>\n" );
document.write( "\n" );
document.write( " Flying 	 Telepathy 	 Super Strength <BR>\n" );
document.write( "Female	78	24	7<BR>\n" );
document.write( "Male	83	40	46<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 telepathy?\r<BR>\n" );
document.write( "\n" );
document.write( "Answer in decimal form.  Round to 3 decimal places as needed<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852323 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=852323\">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': 78, 'Telepathy': 24, 'Super Strength': 7},<BR>\n" );
document.write( "    'Male': {'Flying': 83, 'Telepathy': 40, 'Super Strength': 46}<BR>\n" );
document.write( "}\r<BR>\n" );
document.write( "\n" );
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" );
document.write( "\n" );
document.write( "# 2. Calculate Total Superheroes with Telepathy<BR>\n" );
document.write( "total_telepathy = data['Female']['Telepathy'] + data['Male']['Telepathy']\r<BR>\n" );
document.write( "\n" );
document.write( "# 3. Calculate Empirical Probability of Telepathy<BR>\n" );
document.write( "probability_telepathy = total_telepathy / total_superheroes\r<BR>\n" );
document.write( "\n" );
document.write( "# Print results<BR>\n" );
document.write( "print(f\"Total Superheroes: {total_superheroes}\")<BR>\n" );
document.write( "print(f\"Total Telepathy Superheroes: {total_telepathy}\")<BR>\n" );
document.write( "print(f\"Probability of Telepathy (decimal): {probability_telepathy}\")<BR>\n" );
document.write( "print(f\"Probability of Telepathy (rounded to 3 decimal places): {probability_telepathy:.3f}\")\r<BR>\n" );
document.write( "\n" );
document.write( "```\r<BR>\n" );
document.write( "\n" );
document.write( "```text?code_stdout&code_event_index=2<BR>\n" );
document.write( "Total Superheroes: 278<BR>\n" );
document.write( "Total Telepathy Superheroes: 64<BR>\n" );
document.write( "Probability of Telepathy (decimal): 0.2302158273381295<BR>\n" );
document.write( "Probability of Telepathy (rounded to 3 decimal places): 0.230\r<BR>\n" );
document.write( "\n" );
document.write( "```\r<BR>\n" );
document.write( "\n" );
document.write( "The empirical probability that a randomly selected superhero will have telepathy is calculated by dividing the total number of superheroes with telepathy by the total number of superheroes.\r<BR>\n" );
document.write( "\n" );
document.write( "### 1\. Calculate the Total Number of Superheroes\r<BR>\n" );
document.write( "\n" );
document.write( "$$\begin{aligned} \text{Total Superheroes} &= \text{Total Female} + \text{Total Male} \\ &= (78 + 24 + 7) + (83 + 40 + 46) \\ &= 109 + 169 \\ &= 278 \end{aligned}$$\r<BR>\n" );
document.write( "\n" );
document.write( "### 2\. Calculate the Total Number of Superheroes with Telepathy\r<BR>\n" );
document.write( "\n" );
document.write( "$$\begin{aligned} \text{Total Telepathy} &= \text{Female Telepathy} + \text{Male Telepathy} \\ &= 24 + 40 \\ &= 64 \end{aligned}$$\r<BR>\n" );
document.write( "\n" );
document.write( "### 3\. Calculate the Empirical Probability\r<BR>\n" );
document.write( "\n" );
document.write( "$$\begin{aligned} P(\text{Telepathy}) &= \frac{\text{Total Telepathy}}{\text{Total Superheroes}} \\ &= \frac{64}{278} \\ &\approx 0.230215...\end{aligned}$$\r<BR>\n" );
document.write( "\n" );
document.write( "Rounding to 3 decimal places gives **0.230**. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );