Applied Statistics and Probability for Engineers, 6th Edition

Published by Wiley
ISBN 10: 1118539710
ISBN 13: 978-1-11853-971-2

Chapter 2 - Section 2-4 - Conditional Probability - Exercises: 2-113

Answer

(a) P(A|B)=56/59 (b) P(A'|B)=3/59 (c) P(A|B')=1/2 (d) P(B|A)=14/29

Work Step by Step

266 K 12 40 271 K 44 16 274 K 56 3 A={12, 40, 44, 16}, B={40, 16, 3}, AB={40, 16}, A'={56,3}, B'={12, 44, 56}, P{A|B}=P(AB)/P(B)=$\frac{40+16}{40+16+3}$=56/59, P{A'|B}=1-p{A|B}=3/59 (P(A'|B)=P(A'B)/P(B)=$\frac{3}{40+16+3}$=3/59), P(A|B')=P(AB')/P(B')=$\frac{12+44}{12+44+56}$=1/2, P(B|A)=P(A|B)P(B)/P(A)=$\frac{\frac{56}{59}*59}{12+40+44+16}$=56/116=14/29 (P(B|A)=P(AB)/P(A)=$\frac{40+16}{12+40+44+16}$=56/116=14/29
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.