TCS Company Numerical Ability Permutation and Combination

Paul the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous
accuracy has now been invited to predict ICC world cup matches in 2011. Wewill assume that the world cup
contenders have been divided into 2 groups of 9 teams each. Each team in a group plays the other teams in the
group. The top two teams from each group enter the semifinals ( after which the winner is decided by
knockout).
However, Paul has a soft spot for India and when India plays any team, Paul always backs India. Alas, his
predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it
is sufficient for India to win 7 of its group matches. What is the probability that India will win the ICC world
cup?
a) (2/3)^10
b) (2/3)^9 + 8/3 * (2/3)^9
c) 8/3 * (2/3)^9
d) (2/3)^10 + 8/3*(2/3)^9

Read Solution (Total 2)

Solution is d)
Here winning prob is 2/3 ,so loosing prob is 1/3.

If India win all 10 matches then probability is (2/3)^10
If India loose any one match out of any 8 league matches then probability of winning 7 league matches is (2/3)^7. and for one loose match probability is (1/3).
so these two is also arrange in 8 possible cases, which is arranged as 8{(2/3)^9 * (1/3)}.
Hence total probability is (2/3)^10 + 8/3 * (2/3)^9
9 years agoHelpfull: Yes(2) No(0)

d. (2/3)^10 + 8/3*(2/3)^9

We have two chances to win the world cup. Either India can win all 10matches or Win 7 out of 8 group matches + win the semi final and final matches.

Case 1:

To win all 10, probability is (2/3)^10.

Case 2:

Probability of winning 7mathces out of 8= (2/3)^7 and

Probability of Loosing the 1 match= 1/3.

This process can occur in 8 ways. probability= 8*((2/3)^7 * 1/3)

To win semi final and final match probability is (2/3)^2

Total probability=8*((2/3)^7 * 1/3) * (2/3)^2 = 8/3 * (2/3)^9.

So total probability, Case1+Case 2= (2/3)^10 + 8/3 * (2/3)^9.
9 years agoHelpfull: Yes(1) No(0)

TCS Other Question

Six friends decide to share a big cake. Since all ofthem like the cake, they begin quarreling who gets to
first cut and have a piece of the cake. One friend suggests that they have a blindfold friend choose from well
shuffled set of cards numbered one to six. You check and find that this method works as it should simulating a
fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfold and
throwing a die. You note that the number shown by the method of picking up a card and throwing a real world
die, sums to a number between 2 and 12. Which total would be likely to appear more often – 8,9 or 10?
a) 8
b) All are equally likely
c) 9
d) 10 Asha and Eesha – Eesha lies on Monday, Tuesday and Wednesday. Asha lies on Thursday, Friday and Saturday. Other days they will say the truth. Professor forgot and asked them what day it is. Both of them said yesterday I was lying and then professor got the day. What day it is?