Answer
$P(I~win)=0.5$
There is no advantage given that the coin is fair.
Work Step by Step
$P(I~win)=P(tails~occurs|he~said~heads)P(he~said~heads)+P(heads~occurs|he~said~tails)P(he~said~tails)=0.5\times0.7+0.5\times0.3=0.5$
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
by Larsen, Richard J.; Marx, Morris L.
Published by
Pearson
ISBN 10:
0-13411-421-3
ISBN 13:
978-0-13411-421-7
Chapter 2 Probability - 2.4 Conditional Probability - Questions - Page 45: 35
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