in a tennis match the probability for A to win the match is 2/3 and he has to win 3 sets to win the match so what is the probability for A to win the match

• For A 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. A 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 A 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....A 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
  
  
• 9 years agoHelpfull: Yes(35) No(3)
• howwww...................
  prob of wiing one set is 2/3
  so for 3 sets 2/3*2/3*2/3=8/27
  
• 10 years agoHelpfull: Yes(14) No(16)
• W W W
  L W W W
  W L W W
  W W L W
  L W W L W
  L W L W W
  L L W W W
  W L L W W
  W W L L W
  W L W L W
  total probability is 64/81
• 10 years agoHelpfull: Yes(14) No(14)
• 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 A to win the match as : 192/243. (Ans)
• 9 years agoHelpfull: Yes(10) No(1)
• the answer of this question is 192/243............ i can not doubt now because it is solved by arun sharma friend... bhanu u have missed out few cases whilw calculating please try again
• 10 years agoHelpfull: Yes(3) No(0)
• A wins when out of 5 3 wins and 2 loss.
  so, total of 5 games with 3 wins and 2 loss can be arranged in 5!/(3!*2!)=10 ways
  Out of these 10 games there are 1 match when A wins 3 consecutive sets i.e:WWW and no further matches are played.
  Out of the remaining 9 games there are 3 matches with 4 sets i.e: LWWW
  WLWW WWLW
  so 9-3=6 are played with all 5 sets
  
  therefore
  6*(1/3)^2*(2/3)^3 + 3*(1/3)*(2/3)^3 + (2/3)^3 =192/243 (Ans).
  
• 9 years agoHelpfull: Yes(3) No(0)
• W W W
  L W W W
  W L W W
  W W L W
  L W W L W
  L W L W W
  L L W W W
  W L L W W
  W W L L W
  W L W L W
  total probability is 64/81
  also
  factorise 192/243
  u will get 64/81
  so both are correct
• 9 years agoHelpfull: Yes(2) No(1)
• how do we know there are 5 sets to play..plz sm1 explain.
• 9 years agoHelpfull: Yes(2) No(0)
• Correct question is:
  5 set tennis match(player who wins 3 set win the match. A probibility of winning set is 2/3.what is probibility that A win the match?
• 9 years agoHelpfull: Yes(2) No(0)
• 190/243 is answer
• 10 years agoHelpfull: Yes(1) No(5)
• can anybody tell me why 64/ 81 is wrong.
• 10 years agoHelpfull: Yes(1) No(0)
• 5C3*(2/3)^3*(1/3)^2+4C3*(2/3)^3*(1/3)^1+3C3*(2/3)^3
• 9 years agoHelpfull: Yes(1) No(2)
• bhanu : where is wlwllw in ur solun, and many other combinations like dis
• 9 years agoHelpfull: Yes(1) No(0)
• ans is 8/27
• 9 years agoHelpfull: Yes(1) No(0)
• for a to win 2/3 probability
• 9 years agoHelpfull: Yes(0) No(0)
• xplanatn is not clear
• 9 years agoHelpfull: Yes(0) No(0)