chapter3solutions - STAT 230 Solutions to Problems: Chapter...

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STAT 230 Solutions to Problems: Chapter 3 Note: Questions who solutions are not here are answered sufficiently well in the text. 3.1 a) Notice that you can select the six digits in 7 (6) ways. Now such a number is even if it ends with 2, 4, 6, or 8. Let’s turn the problem around and imagine we build the number from right to left. To obtain an even number then we must start with 2, 4, 6, or 8 . That is we can pick the first digit 4 ways, then the next in 6 then the next in 5 and so on. This results in 4*6*5*4*3*2 ways to pick an even number. The probability then is 7 4 2 3 4 5 6 7 2 3 4 5 6 4 = . Another way: Again, think of building the number from right to left. The probability that you’ll select an even digit first is 4/7 , since 4 of the 7 digits available are even. b) You can have the “2” appear in 5 positions. The “3” is then determined with no choice and you can fill in the remaining 4 positions as usual with the remaining 5 digits. . The number of ways of building such a number is then 5*5*4*3*2 so the probability is 42 5 2 3 4 5 6 7 2 3 4 5 5 = c) Considerably harder, must be done exhaustively. Notice first though that the other 4 spots can still be filled in 5·4·3·2 ways. We need to find how many ways the 2 and 3 can be placed, then multiply by that. If the 2 is the first digit, the 3 has 4 possible locations (remember they can’t be consecutive, so “3” cannot appear 1 st or 2 nd ). If 2 is the second digit, 3 has 3 locations available. It’s not hard to see then that the total number of locations for the 2 and 3 together are: 4+3+2+1 = 10. The probability then is 21 5 2 3 4 5 6 7 2 3 4 5 10 = 3.2 – 3.3 There are 6 4 ways in total they can get off. a) Two stops will have no-one get off, select those stops in 15 2 6 = ways. Then there are 4 stops the first passenger can get off at, 3 for the second … for a total of 4·3·2 = 24 ways. Probability is 18 5 6 ) 24 ( 15 4 = .
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b) Select the two stops 15 2 6 = ways. Then select two people to get off at the first stop
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chapter3solutions - STAT 230 Solutions to Problems: Chapter...

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