Given the following data for an imaginary ssuperhero universe: Flying Telepathy Super Strength Female 89 77 82 Male 17 26 18 Distribution of Super Power by Gender What is the empirical probability that a randomly selected superhero will have telepathy? Answer in decimal form. Round to 3 decimal places as needed

Given the following data for an imaginary ssuperhero universe: Flying Telepathy Super Strength Female 89 77 82 Male 17 26 18 Distribution of Super Power by Gender What is the empirical probability that a randomly selected superhero will have telepathy? Answer in decimal form. Round to 3 decimal places as needed

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Given the following data for an imaginary ssuperhero universe:
Flying Telepathy Super Strength
Female
89
77
82
Male
17
26
18
Distribution of Super Power by Gender
What is the empirical probability that a randomly selected superhero will have
telepathy?
Answer in decimal form. Round to 3 decimal places as needed

Expert Solution

Step 1

According to the fundamental definition of probability,

$P r o b a b i l i t y = \frac{F a v o r a b l e n o . o f o u t c o m e s}{T o t a l n o . o f o u t c o m e s}$

The number of superhero who possess telepathy,

$\begin{array}{rcl} n (T e l e p a t h y s u p e r h e r o e s) & = & n (f e m a l e s u p e r h e r o e s w i t h t e l e p a t h y) + n (m a l e s u p e r h e r o e s w i t h t e l e p a t h y) \\ = & 77 + 26 \\ = & 103 \end{array}$

The total number of superheroes,

$\begin{array}{rcl} T o t a l S u p e r h e r o e s & = & n (f l y i n g s u p e r h e r o e s) + n (t e l e p a t h y s u p e r h e r o e s) + n (s u p e r s t r e n g t h s u p e r h e r o e s) \\ = & n (m a l e f l y i n g s u p e r h e r o e s) + n (f e m a l e f l y i n g s u p e r h e r o e s) + n (m a l e t e l e p a t h y s u p e r h e r o e s) \\ + n (f e m a l e t e l e p a t h y s u p e r h e r o e s) + n (m a l e s u p e r s t r e n g t h s u p e r h e r o e s) \\ + n (f e m a l e s u p e r s t r e n g t h s u p e r h e r o e s) \\ = & 89 + 17 + 77 + 26 + 82 + 18 \\ = & 309 \end{array}$