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barcode font reporting services Method 2 in Software
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Scan QR In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Encode Denso QR Bar Code In C# Using Barcode creator for .NET framework Control to generate, create QR Code ISO/IEC18004 image in VS .NET applications. number of selections of 3 out of 8 red balls number of selections of 3 out of 20 balls
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QR Code JIS X 0510 Creation In Visual Basic .NET Using Barcode generation for .NET Control to generate, create QR Code image in VS .NET applications. Encoding GS1 128 In None Using Barcode maker for Software Control to generate, create EAN / UCC  13 image in Software applications. 14 285 GTIN  13 Encoder In None Using Barcode maker for Software Control to generate, create UPC  13 image in Software applications. Drawing Code39 In None Using Barcode drawer for Software Control to generate, create Code39 image in Software applications. (b) Using the second method indicated in part (a), P(all 3 are white) Encode Barcode In None Using Barcode generation for Software Control to generate, create barcode image in Software applications. Bar Code Generator In None Using Barcode drawer for Software Control to generate, create bar code image in Software applications. 3C3 20C3
Print OneCode In None Using Barcode printer for Software Control to generate, create 4State Customer Barcode image in Software applications. Draw GS1 DataBar In .NET Using Barcode drawer for Visual Studio .NET Control to generate, create DataBar image in VS .NET applications. 1 1140 Decoding Code 128 In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. EAN13 Creator In .NET Using Barcode generation for VS .NET Control to generate, create GTIN  13 image in .NET applications. The first method indicated in part (a) can also be used. (c) P(2 are red and 1 is white) (selections of 2 out of 8 red balls)(selections of 1 out of 3 white balls) number of selections of 3 out of 20 balls (8C2)(3C1) 7 95 20C3 (d) P(none is white) Making Barcode In Java Using Barcode generator for Android Control to generate, create barcode image in Android applications. Creating UPC  13 In VS .NET Using Barcode printer for ASP.NET Control to generate, create EAN13 image in ASP.NET applications. 17C3 20C3
EAN 128 Encoder In Visual C#.NET Using Barcode generator for .NET Control to generate, create GS1128 image in VS .NET applications. Encode Code 128C In ObjectiveC Using Barcode drawer for iPad Control to generate, create Code128 image in iPad applications. 34 . Then 57 P(at least 1 is white) 1 34 57 23 57 (e) P(l of each color is drawn) (8C1)(3C1)(9C1) 20C3
18 95 (f) P(balls drawn in order red, white, blue) Another method
P(R1 > W2 > B3) 1 18 6 95 1 P(l of each color is drawn) 3! 3 , using (e) 95 P(R1) P(W2 u R1) P(B3 u R1 > W2) 8 3 9 20 19 18 3 95 CHAPTER 1 Basic Probability
1.36. In the game of poker 5 cards are drawn from a pack of 52 wellshuffled cards. Find the probability that (a) 4 are aces, (b) 4 are aces and 1 is a king, (c) 3 are tens and 2 are jacks, (d) a nine, ten, jack, queen, king are obtained in any order, (e) 3 are of any one suit and 2 are of another, (f) at least 1 ace is obtained. (a) P(4 aces) (b) (c) (d) (e) 1 . 54,145 (4C4)(4C1) 1 . P(4 aces and 1 king) 649,740 52C5 (4C3)(4C2) 1 . P(3 are tens and 2 are jacks) 108,290 52C5 (4C1)(4C1)(4C1)(4C1)(4C1) 64 . P(nine, ten, jack, queen, king in any order) 162,435 52C5 (4 13C3)(3 13C2) 429 , P(3 of any one suit, 2 of another) 4165 52C5 since there are 4 ways of choosing the first suit and 3 ways of choosing the second suit. 35,673 18,472 35,673 48C5 . Then P(at least one ace) 1 . P(no ace) 54,145 54,145 54,145 52C5 (4C4)(48C1) 52C5 (f ) 1.37. Determine the probability of three 6s in 5 tosses of a fair die.
Let the tosses of the die be represented by the 5 spaces . In each space we will have the events 6 or not 6 (6r). For example, three 6s and two not 6s can occur as 6 6 6r6 6r or 6 6r6 6r6, etc. Now the probability of the outcome 6 6 6r 6 6r is P(6 6 6r 6 6r) P(6) P(6) P(6r) P(6) P(6r) 1 5 6 6 1 1 5 1 5 6 6 6 6 6 since we assume independence. Similarly, P
5 1 6 6 for all other outcomes in which three 6s and two not 6s occur. But there are 5C3 are mutually exclusive. Hence, the required probability is P(6 6 6r6 6r or 6 6r6 6r6 or c) 5C3 6 10 such outcomes, and these
In general, if p P(A) and q 1 p P(Ar), then by using the same reasoning as given above, the probability of getting exactly x A s in n independent trials is nCx p x qn x
1.38. A shelf has 6 mathematics books and 4 physics books. Find the probability that 3 particular mathematics books will be together. All the books can be arranged among themselves in 10P10 10! ways. Let us assume that the 3 particular mathematics books actually are replaced by 1 book. Then we have a total of 8 books that can be arranged among themselves in 8P8 8! ways. But the 3 mathematics books themselves can be arranged in 3P3 3! ways. The required probability is thus given by 8! 3! 10! 1 15 n px qn x
5 6 5! 1 5 3!2! 6 6 125 3888 Miscellaneous problems 1.39. A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a draw. They agree to play a tournament consisting of 3 games. Find the probability that (a) A wins all 3 games, (b) 2 games end in a draw, (c) A and B win alternately, (d ) B wins at least 1 game. Let A1, A2, A3 denote the events A wins in 1st, 2nd, and 3rd games, respectively, B1, B2, B3 denote the events B wins in 1st, 2nd, and 3rd games, respectively. On the basis of their past performance (empirical probability),

