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ssrs 2012 barcode font Find the probability that n people (n in Software
1.45. Find the probability that n people (n QR Code Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. QR Code JIS X 0510 Creator In None Using Barcode generation for Software Control to generate, create QRCode image in Software applications. 365) selected at random will have n different birthdays.
Reading QRCode In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. QR Code Printer In C#.NET Using Barcode generation for Visual Studio .NET Control to generate, create QR image in .NET applications. We assume that there are only 365 days in a year and that all birthdays are equally probable, assumptions which are not quite met in reality. The first of the n people has of course some birthday with probability 365 > 365 1. Then, if the second is to have a different birthday, it must occur on one of the other 364 days. Therefore, the probability that the second person has a birthday different from the first is 364 > 365. Similarly the probability that the third person has a birthday different from the first two is 363 > 365. Finally, the probability that the nth person has a birthday different from the others is (365 n l) > 365. We therefore have P(all n birthdays are different) 365 364 363 c 365 n 365 365 365 365 a1 1 b a1 365 2 b c a1 365 1 n 1 b 365 Encode QRCode In VS .NET Using Barcode drawer for ASP.NET Control to generate, create QR Code 2d barcode image in ASP.NET applications. Generating Quick Response Code In .NET Using Barcode encoder for .NET Control to generate, create Denso QR Bar Code image in .NET applications. 1.46. Determine how many people are required in Problem 1.45 to make the probability of distinct birthdays less than 1 > 2. Draw QR In Visual Basic .NET Using Barcode generator for .NET framework Control to generate, create Denso QR Bar Code image in VS .NET applications. UPC Code Generation In None Using Barcode maker for Software Control to generate, create UCC  12 image in Software applications. Denoting the given probability by p and taking natural logarithms, we find (1) ln p ln a1 1 b 365 ln a1 2 b 365 c ln a1 n 1 b 365 Barcode Creator In None Using Barcode creator for Software Control to generate, create barcode image in Software applications. Create Code39 In None Using Barcode generator for Software Control to generate, create Code 39 image in Software applications. But we know from calculus (Appendix A, formula 7) that (2) ln (1 x) x x2 2 x3 3 c
Generating EAN 13 In None Using Barcode creation for Software Control to generate, create UPC  13 image in Software applications. Data Matrix Generator In None Using Barcode creation for Software Control to generate, create Data Matrix 2d barcode image in Software applications. CHAPTER 1 Basic Probability
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Decode UPC Code In Visual Basic .NET Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications. Drawing Bar Code In Java Using Barcode drawer for Java Control to generate, create bar code image in Java applications. Using the facts that for n (4) 1 2 c
Printing GS1 DataBar Expanded In Java Using Barcode creation for Java Control to generate, create DataBar image in Java applications. Bar Code Generator In None Using Barcode creator for Online Control to generate, create bar code image in Online applications. 2, 3, . . . (Appendix A, formulas 1 and 2) (n 1) n(n 2 1) , 12 22 c (n 1)2 n(n 1)(2n 6 1) Generate Barcode In VS .NET Using Barcode maker for ASP.NET Control to generate, create barcode image in ASP.NET applications. EAN13 Supplement 5 Creation In None Using Barcode generator for Office Excel Control to generate, create UPC  13 image in Microsoft Excel applications. we obtain for (3) (5) ln p n(n 1) 730 n(n 1)(2n 12(365)2 1) c
For n small compared to 365, say, n 30, the second and higher terms on the right of (5) are negligible compared to the first term, so that a good approximation in this case is (6) In p n(n 1) 730 [&!ln!p *frac*{n(n1)}{730}&] For p
1 2, ln p
ln 2
0.693. Therefore, we have
n(n 1) 730 23)(n
so that n 23. Our conclusion therefore is that, if n is larger than 23, we can give better than even odds that at least 2 people will have the same birthday. SUPPLEMENTARY PROBLEMS
Calculation of probabilities
1.47. Determine the probability p, or an estimate of it, for each of the following events: (a) A king, ace, jack of clubs, or queen of diamonds appears in drawing a single card from a wellshuffled ordinary deck of cards. (b) The sum 8 appears in a single toss of a pair of fair dice. (c) A nondefective bolt will be found next if out of 600 bolts already examined, 12 were defective. (d ) A 7 or 11 comes up in a single toss of a pair of fair dice. (e) At least 1 head appears in 3 tosses of a fair coin. 1.48. An experiment consists of drawing 3 cards in succession from a wellshuffled ordinary deck of cards. Let A1 be the event king on first draw, A2 the event king on second draw, and A3 the event king on third draw. State in words the meaning of each of the following: (a) P(A1 > Ar2 ), (b) P(A1 < A2), (c) P(Ar1 < Ar2 ), (d) P(Ar1 > Ar2 > Ar3), (e) P[(A1 > A2) < (Ar2 > A3)]. 1.49. A marble is drawn at random from a box containing 10 red, 30 white, 20 blue, and 15 orange marbles. Find the probability that it is (a) orange or red, (b) not red or blue, (c) not blue, (d) white, (e) red, white, or blue. 1.50. Two marbles are drawn in succession from the box of Problem 1.49, replacement being made after each drawing. Find the probability that (a) both are white, (b) the first is red and the second is white, (c) neither is orange, (d) they are either red or white or both (red and white), (e) the second is not blue, (f) the first is orange, (g) at least one is blue, (h) at most one is red, (i) the first is white but the second is not, ( j) only one is red.

