Latest TCS Aptitude Question SOLUTION: 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

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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

Asked In TCS sundeep (10 years ago)

Solved bhanu prakash reddy a Read Solution (16)

Is this Puzzle helpful?   (8)   (4) Submit Your Solution Probability

Read Solution (16) :

Devang  (9 years ago)

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

Is this solution Helpfull? Yes (35) | No (3)  

sundeep  (10 years ago)

howwww...................
prob of wiing one set is 2/3
so for 3 sets 2/3*2/3*2/3=8/27

Is this solution Helpfull? Yes (14) | No (16)  

bhanu prakash reddy a  (10 years ago)

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

Is this solution Helpfull? Yes (14) | No (14)  

Debdutta Das  (9 years ago)

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)

Is this solution Helpfull? Yes (10) | No (1)  

chanchal singh  (10 years ago)

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

Is this solution Helpfull? Yes (3) | No   

Koustav  (9 years ago)

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).

Is this solution Helpfull? Yes (3) | No   

Vaibhav kumar   (9 years ago)

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

Is this solution Helpfull? Yes (2) | No (1)  

nandita shrivastava  (9 years ago)

how do we know there are 5 sets to play..plz sm1 explain.

Is this solution Helpfull? Yes (2) | No   

Lavanyaa Sharma  (9 years ago)

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?

Is this solution Helpfull? Yes (2) | No   

chanchal singh  (10 years ago)

190/243 is answer

Is this solution Helpfull? Yes (1) | No (5)  

bhanu prakash reddy a  (10 years ago)

can anybody tell me why 64/ 81 is wrong.

Is this solution Helpfull? Yes (1) | No   

vrajesh  (9 years ago)

5C3*(2/3)^3*(1/3)^2+4C3*(2/3)^3*(1/3)^1+3C3*(2/3)^3

Is this solution Helpfull? Yes (1) | No (2)  

Ritu Jha  (9 years ago)

bhanu : where is wlwllw in ur solun, and many other combinations like dis

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karthik Kumar reddy  (9 years ago)

ans is 8/27

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am  (9 years ago)

for a to win 2/3 probability

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Adhmega  (9 years ago)

xplanatn is not clear

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