answers

MATH ,MATHEMATICAL ANALYSIS

1 . Evaluate the following factorials , permutations , and combinations (f ) 12P3 2 . How many different 4-letter radio station call letters can be made (a ) if the first letter must be K or W and no letter may be repeated (b ) if repeats are allowed (but the first letter is K or W

3 . A baseball team has 20 players . How many 9-player batting s are possible

4 . A shipment of 9 computers contains 2 with defects . Find the probability that a sample of the following size , drawn from the 9 , will

contain a defective (a ) 2 (b ) 4

5 . A grab bag contains 10 1 prizes , 6 5 prizes , and 2 20 prizes Three prizes are randomly drawn . Find the following probabilities (a ) All 5 prizes (b ) One prize of each kind (c ) No 1 prize 6 . A bridge hand consists of 13 cards from a deck of 52 . Set up the probabilities that a bridge hand includes each of the following (a ) 6 face cards (b ) 7 cards of one suit and 6 of another

7 . A die is rolled 12 times . Find the probability of rolling (a ) Exactly 6 ones (b ) Exactly 2 ones (c ) No more than 1 one

8 . A survey finds that customers in a supermarket overpay for 1 out of every 10 items , on average . Suppose a customer purchases 15 items Find the following probabilities (a ) A customer does not overpay for any item (b ) A customer overpays on at least 2 items

1

a ) 3 6

b ) 7 5040 8 (d ) 4P4 24 45 (f ) 12P3 1320

2

a ) 2 25 24 23 27600

b ) 2 26 26 26 35152 3 . 20P9 6 . 1010

4

a ) 1 / 9C2 1 /36 0 .0277

b ) 4C2 /9C4 6 /126 0 .00476

5

a )6C3 /18C3 20 /816

b (10C1 6C1 2C1 / 18C3 120 /816

c )8C3 /18C3 56 /816

6

a (12C6 46C7 /52C13

b (1 /4 13C7 (1 /3 13C6 / 52C13

7

a (12C6 (1 /6 )6 (5 /6 )6

b (12C2 (1 /6 )2 (5 /6 )10

c (12C1 (1 /6 (5 /6 )11

8

a (9 /10 )15

b ) 1- [ (12C1 (1 /10 (9 /10 )11 (12C2 (1 /10 )2 (9 /10 )10 )]...