Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 5 - Section 5.1 - Assess Your Understanding - Explaining the Concepts - Page 268: 60


(b) Switch.

Work Step by Step

In the beginning: The sample space: S={envelope 1, envelope 2, envelope 3, envelope 4}. So, $N(S)=4$ Event E = "My envelope contains 100 dollars". So, $N(E)=1$ Event F = "My envelope does not contain 100 dollars". So, $N(F)=3$ $P(E)=\frac{N(E)}{N(S)}=\frac{1}{4}=0.25$ $P(F)=\frac{N(F)}{N(S)}=\frac{3}{4}=0.75$ The game host discards two empty envelopes. The probability that the remaining envelope is the one which contains $100 is 75% because it is one of the three remaining envelopes. That is, if you have chosen a "wrong" envelope (P(F)=75%) you can switch the envelopes and get the "right" one.
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