Asked on 17th JAN, 2016

A number is of form abbbbbba , where a is not equal to b, and neither a nor b equals 0(zero). eg. 12222221 . What is the probability that such possible numbers are divisible by 3.

• i think
  (2a+6b)/3
  2a/3+6b/3 (6b alwayes divisible by 3, so we have chek only for 3a part)
  2a/3 divisible by 3 only when
  a is multiple of 3 like a=3,6,9
  so we have only three condition at which (2a+6b) or abbbbbba will divisible 3
• 9 years agoHelpfull: Yes(38) No(0)
• total of such numbers = 72
  no. of such numbers = 24
  probablity = 1/3
• 9 years agoHelpfull: Yes(30) No(7)
• Ans: 1/3
  
  a can be any of the 9 numbers from (1,2,3,...,9).
  b can be any of the remaining 8 numbers.
  total: 9×8 = 72
  
  i.e., there can be 72 possible numbers.
  
  If the number is divisible by 3,
  a+b+b+b+b+b+b+a is divisible by 3.
  => 2a + 6b is divisible by 3.
  => 2a is divisible by 3 (because 6b is always divisible by 3).
  => a can be (3,6,9)
  
  Thus, if the number is divisible by 3,
  a can be any of the 3 numbers from (3,6,9).
  b can be any of the 8 remaining numbers.
  total: 3×8 = 24
  
  i.e., there can be 24 possible numbers which are divisible by 3
  
  Required probability =24/72=1/3
• 8 years agoHelpfull: Yes(29) No(1)
• answer 8/27
  i dont know whether this is correct or not but here is what according to me can be the way to solve it.
  a number to be divisible by 3 sum of its unit digit must be divisible by 3 therefore
  6b+2a=3z
  dividing above equation by 3 we get
  2b+2/3a=z
  2/3a should be integer therefore a can only be 3,6,9.
  now
  if a=3
  probablity of selecting 3 is 1/9
  probality of selecting any number other than 3 for b is 8/9
  so 1/9*8/9=8/81
  similiarly we will do for a= 6 and a=9
  and we will get 8/81 for all of them.
  now we will add all the three
  3(8/81)
  hence answer is 8/27
• 9 years agoHelpfull: Yes(8) No(0)
• @Dytort: The total number of such numbers are 72 ? how ? It should be 36 instead !
• 9 years agoHelpfull: Yes(1) No(0)
• ~The total no. Of such numbers should be- 9×8×1×1×1×1×1×1= 72
  ~The number of such numbers divisible by 3 will be-
  1) By keeping 3 at 1st and last place- 9numbers
  2) By keeping 6 at 1st and last place- 9 numbers
  3) By keeping 9 at 1st and last place- 9numbers
  so total of such numbers= 9+9+9= 27
  ~ Probability= 72/27 = 8/3
• 9 years agoHelpfull: Yes(1) No(5)
• total such nos=72
  no. of such numbers will be 24
  hence p=24/72
• 8 years agoHelpfull: Yes(1) No(0)
• total of such numbers = 36
  no. of such numbers = 24
  probability = 2/3
  
  (3c1*8c1)/9c2
  
• 9 years agoHelpfull: Yes(0) No(2)
• @Deepak how 9. If u have already chose a number and ques says that a & b cant be 0
  
• 8 years agoHelpfull: Yes(0) No(0)
• Here b can be any value between 0-9 and a can be only multiple of 3 i.e 3,6,9.
  So probability depends upon what value a take i.e 3/10
  Hence ans is 3/10.
• 6 years agoHelpfull: Yes(0) No(0)