Eric throw two dice and his score is the sum of the values shown.Sandra throws one die and her score is the square of the value shown. what is the probability that sandra score will be strictly higher than eric score?

• ANSWER: 137/216
  EXPLANATION
  -----------
  Probability of SANDRA winning is 1 if she gets 4,5 or 6.
  Probability of SANDRA winning is 0 if she gets a 1
  P(Sandra wins if she gets 2)= ?
  P(Sandra wins if she gets 3)= ?
  SANDRA GETS '2'
  ---------------
  Favourable events are if ERIK gets (1,1),(1,2) or (2,1)
  Total no of favourable events= 3
  Probability= 3/36 where 36 is coz total 36 events are poosible
  SANDRA gets a '3'
  -----------------
  She wins if Erik does not get (6,6),(6,5)(5,6),(6,4),(4,6)(5,5),(6,3),(3,6),(4,5),(5,4)........... Total= 36-10= 26 favorable events
  Therefore probability = 26/36.
  -------------------------
  Probabilty of Sandra getting any of the 6 nos is 1/6.
  HENCE, PROBABILTY THAT SANDRA WINS
  =(1/6 * 0)+(1/6 * 3/36)+(1/6 * 26/36)+(1/6 * 1)+(1/6 * 1)+(1/6 * 1)= 137/216
• 10 years agoHelpfull: Yes(156) No(18)
• Sandra's possible scores-
  1 (1)
  4 (2)
  9 (3)
  16 (4)
  25 (5)
  36 (6)
  
  So for Sandra's score=1 there will be no favorable outcomes as Eric score will always be >=2 with 2 being his least score for dice throws of 1 and 1 on both dice.
  
  Similarly for X=4 (Sandra's score)
  Dices throw of (1,1) , (1,2) , (2,1) are favorable cases.
  so P(X=4)= 3/36* 1/6= 3/216
  [ 1/6 is the probability of getting 2 on a throw of dice by Sandra (and hence the score=4) and 3 outcomes are favorable out of 36 for Eric's throw of 2 dice.
  
  Same with X=9
  Favorable Cases- (1,1), (1,2) ,(1,3) ,(1,4) ,(1,5) ,(1,6) ,(2,1) ,(2,2) ,(2,3) ,(2,4) ,(2,5) ,(2,6) ,(3,1) ,(3,2) ,(3,3) ,(3,4) ,(3,5) ,(4,1) ,(4,2) ,(4,3) ,(4,4) ,(5,1) ,(5,2) ,(5,3) ,(6,1) ,(6,2)
  so P(X=9)= 26/36*1/6 = 26/216
  
  For X=16, 25,36
  all cases are favorable as the max score of Eric can be 12 (6,6)
  Hence P(X=16)=P(X=25)=P(X=36)= 1/6* 36/36=36/216
  
  So adding all the cases-
  3/216 + 26/216 + 36/216 +36/216 + 36/216 = 137/216 (Ans)
• 8 years agoHelpfull: Yes(30) No(1)
• definitely higher.
  
  36+36+36 = 108 ways
  
  If she scores 1,
  
  Eric's score will always be greater.
  
  If she scores 4,
  
  her score will be higher only if Eric scores (1,1), (1,2) or (2,1)
  
  3 ways
  
  If she scores 9,
  
  Eric's score will be greater if he scores (3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), (6,6)
  
  Eric's score will be lesser in (36-10 =)26 ways.
  
  n(E) = 108+0+3+26
  
  = 137
  
  n(S) = No. of ways of throwing three dice
  
  = 6*6*6 = 216
  
  P(E) = 137/216
• 8 years agoHelpfull: Yes(8) No(0)
• 1/2....coz sandra win whn she got 4,5,6 on her dice.....othwise condtn not satisfied ....maximum geting for eric is 12
• 10 years agoHelpfull: Yes(4) No(36)
• plz explain clearly
  
• 9 years agoHelpfull: Yes(4) No(2)
• ANSWER 1/2
  sandra wins if she brings 4,5,6 on her dice else she losses
  we will not consider 36 cases for eric as we r interested in only scores not the way it came , hence (6,3) and (3,6) will be one case of outcome being 9 .
  so i think answer should be 1/2
• 9 years agoHelpfull: Yes(2) No(15)
• 1/2....
  if 1,2,3 come to sandra then only she will loose
• 10 years agoHelpfull: Yes(1) No(28)
• definitely higher.
  
  36+36+36 = 108 ways
  
  If she scores 1,
  
  Eric's score will always be greater.
  
  If she scores 4,
  
  her score will be higher only if Eric scores (1,1), (1,2) or (2,1)
  
  3 ways
  
  If she scores 9,
  
  Eric's score will be greater if he scores (3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), (6,6)
  
  Eric's score will be lesser in (36-10 =)26 ways.
  
  n(E) = 108+0+3+26
  
  = 137
  
  n(S) = No. of ways of throwing three dice
  
  = 6*6*6 = 216
  
  P(E) = 137/216
• 6 years agoHelpfull: Yes(1) No(0)