10. A six faced die is so biased that it is twice as likely to show an even number as an odd. It is thrown twice. What is the probability that the sum of the numbers is even?
a) 1/3 b) 2/3 c) 5/9
d) 6/11

• Probability of getting an even number = 2/3
  Probability of getting an odd number = 1/3
  since the dice is biased.
  The sum is even if
  (even,even) or (odd,odd)
  [P(even).P(even)] + [P(odd).P(odd)]
  2/3 * 2/3 + 1/3 * 1/3 = 4/9 + 1/9 = 5/9
• 9 years agoHelpfull: Yes(49) No(0)
• ((2/3).(2/3))+((1/3).(1/3)=5/9
• 9 years agoHelpfull: Yes(7) No(4)
• Probability for odd = p
  ∴ Probability for even = 2p
  ∵ p + 2p = 1
  ⇒ 3p = 1
  ⇒ p = 1/3
  
  ∴ Probability for odd = 1/3, Probability for even = 2/3.
  Sum of two nos. is even means either both are odd or both are even
• 7 years agoHelpfull: Yes(5) No(0)
• die is biased i.e twice for even so 4/6 = 2/3
  for odd = 2/6 =1/3
  prob of even = o*o or e*e
  2/3*2/3+1/3*1/3=5/9
• 9 years agoHelpfull: Yes(2) No(0)
• (1,1) (1,3) (1,5) 2,2 2,4 2,6 like this we can get 18 no of sets . Total no of possible outcome is 6x6 36
  So It should be 18/36 = 1/2
  Why 5/9 ? Please explain
• 9 years agoHelpfull: Yes(1) No(1)
• Probability for odd = p
  ∴ Probability for even = 2p
  ∵ p + 2p = 1
  ⇒ 3p = 1
  ⇒ p = 1/3
  
  ∴ Probability for odd = 1/3, Probability for even = 2/3.
  Sum of two nos. is even means either both are odd or both are even
  so The sum is even if
  (even,even) or (odd,odd)
  [P(even).P(even)] + [P(odd).P(odd)]
  2/3 * 2/3 + 1/3 * 1/3 = 4/9 + 1/9 = 5/9
• 5 years agoHelpfull: Yes(1) No(0)
• 5/9 is d ri8 Answer
• 9 years agoHelpfull: Yes(0) No(0)