5 set tennis match(player who wins 3 set win the match. rams probibility of winning set is 2/3.what is probibility that ram win the match?

• For Ram to win a match he has to win minimum 3 sets.....So minimum 3 sets will be played
  
  Case 1---->The match is completed in 3 sets only i.e. Ram wins first 3 sets.
  So,W W W case
  probability=2/3 * 2/3 * 2/3 = 8/27-----1
  
  Case 2------> The match is completed in 4 sets i.e Ram wins 3 sets from 4 sets played and losses 1 set ...This can be done in 3 ways....
  W W L W
  W L W W
  L W W W
  probability in one such cases=2/3 * 2/3 *2/3 * 1/3= 8/81
  So, probability in 3 cases = 3 * 8/81 = 24/81-------->2
  
  
  Case 3----->Now all 5 sets are played....Ram wins 3 sets and losses 2 sets...This can be done following 6 cases..
  W W L L W
  W L W L W
  W L L W W
  L W W L W
  L W L W W
  L L W W W
  
  probability in one such case = 2/3 * 2/3 * 2/3 * 1/3 * 1/3 = 8/243
  
  so, probability in 6 cases = 6 *8/243 =48/243--------->3
  
  Sp, final probability=1+2+3
  = 8/27 + 24/81 + 48/243
  = 192/243----Ans
• 10 years agoHelpfull: Yes(25) No(3)
• we also have to think that he may also win all of the Sets.Considering the OR situation, we will add up all of the possibilities as
  =5C3*(2/3)^3*(1/3)^2+5C4*(2/3)^4*(1/3)^1+5C3*(2/3)^5*(1/3)^0
  =64/81
  
• 10 years agoHelpfull: Yes(11) No(3)
• 5C3*(2/3)^3*(1/3)^2 is the ans
• 10 years agoHelpfull: Yes(6) No(9)
• The sequence of winning as follows:
  
  
  Sequence Probability
  ------- -----------
  
  W W L W : 8/81
  W W L L W : 8/243
  W W W : 8/27
  W L L W W : 8/243
  W L W L W : 8/243
  W L W W : 8/81
  L L W W W : 8/243
  L W L W W : 8/243
  L W W L W : 8/243
  L W W W : 8/81
  
  
  Thus, by adding all the above probabilities, we get the probability for Ram to win the match as : 192/243. (Ans)
• 10 years agoHelpfull: Yes(2) No(0)