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: 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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.