Latest TCS Aptitude Question SOLUTION: 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?

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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?

Asked In TCS chanchal singh (10 years ago)

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Read Solution (4) :

Devang  (9 years ago)

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

Is this solution Helpfull? Yes (25) | No (3)  

Poonam Rathore  (10 years ago)

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

Is this solution Helpfull? Yes (11) | No (3)  

Jasmeet  (10 years ago)

5C3*(2/3)^3*(1/3)^2 is the ans

Is this solution Helpfull? Yes (6) | No (9)  

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 Ram to win the match as : 192/243. (Ans)

Is this solution Helpfull? Yes (2) | No   

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