Answered: If o(E) = 5:7, find o(E'). o(E') =

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If o(E) = 5:7, find o(E'). o(E') =

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 18EQ

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Question

If o(E) = 5:7, find o(E').
o(E') =

Expert Solution

Step 1

The formula for odds of event E is,

$o (E) = \frac{P (E)}{1 - P (E)}$

The odds of E can be written as, $m : n o r \frac{m}{n}$ .

The probability of event E is obtained as,

$\begin{array}{rcl} o (E) & = & \frac{P (E)}{1 - P (E)} \\ \frac{5}{7} & = & \frac{P (E)}{1 - P (E)} \\ 5 (1 - P (E)) & = & 7 P (E) \\ 5 P (E) + 7 P (E) & = & 5 \\ 12 P (E) & = & 5 \\ P (E) & = & \frac{5}{12} \end{array}$

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