two numbers are selected at random from the integers 1 through 9 the sum is even. what is the probability of both are odd?

• 1 2 3 4 5 6 7 8 9
  chances that the sum is even= 41. since there are 81 possibilities(9*9) and 41 in them are even sum.
  chances that both number are odd is 25(5*5)
  therefore,probability= 25/41.
• 11 years agoHelpfull: Yes(2) No(1)
• the above submitted ans is wrong . this is correct
  
  let two no's are a,b
  so sum of a,b is even
  sum of two no's is even only when two no's are either even or odd
  even no : 2,4,6,8
  possibilties are if a = 2 then b have 4 values 2,4,6,8 so 4 possobilities exists
  so 4*4 = 16
  odd no : 1,3,5,7,9
  similarly
  if a=1 then b has 5 values
  so 5*5=25 posssibilities when both are odd
  so prob(a,b are odd) = 25/(25+16)= 25/41
• 11 years agoHelpfull: Yes(2) No(1)
• ANS=5/8
  Here it is just selection.So the order in which we take the numbers is not important.
  Combinations of numbers which give even sum:
  (1,3)(1,5)(1,7)(1,9)(3,5)(3,7)(3,9)(5,7)(5,9)(7,9)(2,4)(2,6)(2,8)(4,6)(4,8)(6,8)
  There are totally 16 combinations
  Out of these 10 pairs are odd numbers
  Thus probability= 10/16 = 5/8
  ANS= 5/8
• 11 years agoHelpfull: Yes(2) No(2)
• 1 2 3 4 5 6 7 8 9
  so odd no are 1 3 5 7 9
  so no of cases with odd no =25
  and total no of cases =81(9*9)
  p=25/81
  
• 11 years agoHelpfull: Yes(0) No(1)
• the answer is more than 3/8.
• 11 years agoHelpfull: Yes(0) No(2)
• let two no's are a,b
  so sum of a,b is even
  sum of two no's is even only when two no's are either even or odd
  even no : 2,4,6,8
  possibilties are if a = 2 then b have 3 values 4,6,8 so 3 possobilities exists
  so 4*3 = 12
  odd no : 1,3,5,7,9
  similarly
  if a=1 then b has 4 values
  so 4*4=16 posssibilities when both are odd
  so prob(a,b are odd) = 16/(16+12)= 4/7
• 11 years agoHelpfull: Yes(0) No(2)