Question

nicole has a machine that will produce a number from 1 through 50 when she pushes a button. p(multiple of 10)? A. p(not 100)? B. p( not multiple of 4) ? C. p( one digit number)?

Answer 1

Nicole has a machine that will produce a number from 1 through 50 when she pushes a button. p(multiple of 10)? A. p(not 100)? B. p( not multiple of 4) ? C. p( one digit number)? 
a) the possibilities that the number will be a multiple of 10 are:
    favorable cases: 5 (there are 5 numbers that are multiples of 10 from 1 to 50: 10, 20, 30, 40, 50)
   possible cases: 50 (there are 50 numbers from 1 to 50)
  possibilities that the number will be a multiple of 10: $\frac{5}{50}$⁽₅ = $\frac{1}{10}$

 there are 10% that the number which will be produced after Nicole will push the button will be a multiple of 10

b)  the possibilities that the number won't be 100 
   favorable cases = 50 (no number from 1 to 50 is 100) 
   possible cases = 50 (there are 50 from 1 to 50)  
possibilities that the number won't be 100: $\frac{50}{50}$⁽⁵⁰ = $\frac{1}{1}$ 

 there are 100% that the number which will be produced after Nicole will push the button won't be 100

c)  the possibilities that the number won't be a multiple of 4
favorable cases: 50 - 12 = 38 (12 numbers from 1 to 50 are multiples of 4)
possible cases: 50
possibilities that the number won't a multiple of 4: $\frac{38}{50}$

there are 76% that the number which will be produced after Nicole will push the button won't be a multiple of 4                                                                                                                                                                                                                                                                                                                   d)  the possibilities that the number will be an one digit number
      favorable cases: 9 (there are 9 one digit numbers from 1 to 50)                    possible cases: 50 (there are 50 numbers from 1 to 50)                                 possibilities that the number will be an one digit number:  $\frac{9}{50}$
                                                                                                                                 there are 18% that the number which will be produced after Nicole will push the button will be an one digit number