a,b,c, chosen randomly and with replacement from the set {1,2,3,4,5},the probablity that a*b+c is even

• 4 cases:
  {odd,odd,even}
  {odd,even,even}
  {even,even,even}
  {even,odd,even}
  3/5*3/5*3/5 + 3/5*2/5*2/5 + 2/5*2/5*2/5 + 2/5*3/5*2/5
  =(27+12+8+12)/125
  =59/125
• 12 years agoHelpfull: Yes(13) No(18)
• For a*b + c to be even, we require either that both a*b and c are odd, or that
  both a*b and c are even.
  
  Case 1: a*b is odd only when both a and b are odd. As there are 3 odd number
  in the set given, there will be 3*3 = 9 combinations of odd numbers out of a
  total of 5*5 = 25 combinations with no restrictions for a probability of 9/25.
  Next, since there are 3 odd numbers in the given set, the probability that c
  is odd is 3/5.
  
  Case 2: a*b is even when at least one of a or b is even. This is the same as
  saying that a*b is even when a*b is not odd, so there are 25 - 9 = 16 combinations
  that make a*b even. The probability that c is even is 2/5.
  
  Thus, combining these two cases, the probability that a*b + c is even is
  (9/25)(3/5) + (16/25)(2/5) = (27/125) + (32/125) = 59/125 or 47.2 %.
• 12 years agoHelpfull: Yes(10) No(1)
• conditions:
  1. All the values of a,b,c are ODD
  2. C is odd.. "atleast" one of a and b should be odd
  i.e, if a is odd, b can be anything
  if b is odd, a can be anything
  
  Probability(a*b*c):(3/5 * 3/5 * 3/5) + ( 2/5 * 5/5 * 2/5 ) + (5/5 * 2/5 * 2/5)
  solving it.. = 67/125 //
  
  
• 12 years agoHelpfull: Yes(7) No(6)
• If all the values of a,b,c is EVEN then a*b+c this term EVEN
  or all the values of a,b,c is ODD then a*b+c this term EVEN
  now we can select even term form 1,2,3,4,5 by 2*2*2 = 8 ways
  or select odd term from 1,2,3,4,5 by 3*3*3 = 27 ways
  So the total selection is (8+27) = 35 out of 5*5*5*5*5= 5^5
  so the probability is 35/(5^5)
• 12 years agoHelpfull: Yes(2) No(6)
• @ RIMAN,
  
  Why hv you not considered the case when one of a,b is even and other is odd ?
• 12 years agoHelpfull: Yes(2) No(4)
• @ RIMAN,
  
  Why hv you not considered the case when one of a,b is even and other is odd and C is even ?
• 12 years agoHelpfull: Yes(2) No(2)
• the probability is=47/125
• 12 years agoHelpfull: Yes(0) No(1)
• Cases {e,e,e}+{o,e,e}×2 +{o,o,o}
  (2/5*2/5*2/5 +3/5*3/5*3/5+(2/5/2/5*3/5)*2
  =
  59/125
  =0.472
• 5 years agoHelpfull: Yes(0) No(0)