# PS2s - SOLUTIONS TO ISMT111 PROBLEM SET #2 (1) Ans: 0.005....

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: SOLUTIONS TO ISMT111 PROBLEM SET #2 (1) Ans: 0.005. Let event A: getting by the ﬁrst inspector; event B: getting by the second inspector; Given P (A) = 0.05; P (B ) = 0.10, and the two events are independent. P (getting by both inspectors) = P (A ∩ B ) = P (A)P (B ) = 0.005 because A & B are independent (2) Ans: 0.0690. P (I ∪ II ∪ III ) = P (I ) + P (II ) + P (III ) − P (II ∩ III ) − P (I ∩ II ) − P (I ∩ III ) + P (I ∩ II ∩ III ) = .02 + .01 + .04 − (.02)(.01) − (.02)(.04) − 0 + 0 = .0690. (3) Ans: 0.050 Let event L: local newspaper; event C: city newspaper; Given P (L) = 0.65; P (C ) = 0.40. The question is P (subscribe to both) = P (L ∩ C ) =? P (subscribe to a newspaper) = P (L ∪ C ) = 1. P (L ∪ C ) = P (L) 1 = 0.65 + + P (C ) 0.40 − P (L ∩ C ) ; − P (L ∩ C ) , P (L ∩ C ) = 0.65 + 0.40 − 1 = 0.05 Alternatively, draw a Venn diagram: two overlapping circles, one representing L (say, area=650), the other representing C (say, area=400). The combined area is 1,000. So the overlapping area=50. (4) Answer: 0.97 = 0.85 + 0.15 × 0.80 (Draw a Venn diagram.) = P (A ∩ B ) (5) Answer: 12.00% A : The S & P Index rises in value by more than 15%. P (A) = 0.20. B : The mutual fund rises in value by more than 15%. P (B ) = 0.60. At this point, you cannot simply set P (A∩B ) equal to P (A)×P (B ) unless you have evidence to show that A and B are independent. Instead, the table below gives P (A ∩ B ) = 12/100. B A Ac (6) A and B are not mutually exclusive because P (A ∩ B ) = 0. A and B are independent because P (B ) = 0.6 and P (B |A) = 12/20 = 0.6 = P (B ). ∗ ∗ 1 ∗ ATChan 2008 12 √ 60 Bc 8 √ (.40 × 80) = 32 40 √ 20 80 100 ...
View Full Document

## This note was uploaded on 12/22/2009 for the course ISOM ISOM111 taught by Professor Anthonychan during the Fall '09 term at HKUST.

Ask a homework question - tutors are online