Official Quant thread for CAT 2013

Suppose a car salesmen tell the truth 2/5 of the time, and 1/3 of the trees in a forest are oak. If 4 car salesmen say that a certain tree in the forest is oak, what is the probability that the tree is indeed oak?
For a change...Options:
1) 4/89
2) 8/89
3) 16/89
4) 15/178
@nick_baba said:
and put x=y=1/2..still k will be odd integer and x^2 + y^2 will be 1/2..
bhai x and y are non-negative integers !
@techsurge said:
whats the answer is it not 2k^2 +1/2 ?
Its (((k-1)/2)^2)+(((k+1)/2)^2)
@techsurge said:
whats the answer is it not 2k^2 +1/2 ?
It's (k^2+1)/2 😃 Apne kahi kuch galti kari h shayad..
@ScareCrow28 said:
It's (k^2+1)/2 Apne kahi kuch galti kari h shayad..
found my mistake
instead of k/2-1/2 i took k-1/2
@ScareCrow28 said:
Suppose a car salesmen tell the truth 2/5 of the time, and 1/3 of the trees in a forest are oak. If 4 car salesmen say that a certain tree in the forest is oak, what is the probability that the tree is indeed oak?
16/625...?

OR 16/97?
@ayushnasa said:
16/625...?
Please have a look at the options.. :)
@ScareCrow28 said:
Suppose a car salesmen tell the truth 2/5 of the time, and 1/3 of the trees in a forest are oak. If 4 car salesmen say that a certain tree in the forest is oak, what is the probability that the tree is indeed oak?For a change...Options:1) 4/892) 8/893) 16/894) 15/178
1/3*(2/5)^4/(1/3*(2/5)^4+2/3*(3/5)^4)
=16/(16+162)
=16/178
=8/89

oh...:| Probability :banghead:

@krum bhai Khub tayaari chalri hai IIFT ki!! Lage raho..bhot upar jaoge..
@ScareCrow28 said:
Suppose a car salesmen tell the truth 2/5 of the time, and 1/3 of the trees in a forest are oak. If 4 car salesmen say that a certain tree in the forest is oak, what is the probability that the tree is indeed oak?For a change...Options:1) 4/892) 8/893) 16/894) 15/178
8/89
@ScareCrow28 said:
@krum bhai Khub tayaari chalri hai IIFT ki!! Lage raho..bhot upar jaoge..
bhaiya abhi halat kharab hai, pm mein batata hun bad mein
@ScareCrow28 said:
Suppose a car salesmen tell the truth 2/5 of the time, and 1/3 of the trees in a forest are oak. If 4 car salesmen say that a certain tree in the forest is oak, what is the probability that the tree is indeed oak?For a change...Options:1) 4/892) 8/893) 16/894) 15/178

(they are speaking truth)/(they are speaking truth + they are lying)

(1/3*2/5*2/5*2/5*2/5)/(1/3*2/5*2/5*2/5*2/5 + 2/3*3/5*3/5*3/5*3/5)

= 16/178 = 8/89


Three men toss a coin in succession for a prize to be given to the person who first obtains a head. What is each man's chance of winning the prize?
@ScareCrow28 said:
Three men toss a coin in succession for a prize to be given to the person who first obtains a head. What is each man's chance of winning the prize?
1/2 , 1/4. 1/8 ?
A mouse has 3 rooms to go into.
If it goes into room 1 it will find the cheese after 3 minutes.
If it goes into room 2 it will look for cheese for 4 minutes, won't find it, and will go out.
If it goes into room 3 it will look for cheese for 5 minutes, won't find it, and will go out.

The mouse will not remember that it was in rooms 2 and 3 after it goes out of them, and it will continue going in and out until it finds the cheese. (It can go into the same room again and again.)

What is the average time for the mouse to find cheese?
@ScareCrow28 said:
Three men toss a coin in succession for a prize to be given to the person who first obtains a head. What is each man's chance of winning the prize?
1st man-4/7
2nd man-2/7
3rd man-1/7??????
@ScareCrow28 said:
Three men toss a coin in succession for a prize to be given to the person who first obtains a head. What is each man's chance of winning the prize?
1st man's - 1/2+1/2^4+1/2^7+..=1/2/(1-(1/2)^3)=1/2/(7/8)=4/7
2nd man's - 1/2^2+1/2^5+1/2^8..=1/2^2/(1-(1/2)^3)=2/7
3rd man's - 1/7

Solutions padh ke to samajh mein aa rahe hai Probability ke questions, khud se nhi ho rahe :banghead:

@ScareCrow28 said:
A mouse has 3 rooms to go into. If it goes into room 1 it will find the cheese after 3 minutes. If it goes into room 2 it will look for cheese for 4 minutes, won't find it, and will go out. If it goes into room 3 it will look for cheese for 5 minutes, won't find it, and will go out.The mouse will not remember that it was in rooms 2 and 3 after it goes out of them, and it will continue going in and out until it finds the cheese. (It can go into the same room again and again.)What is the average time for the mouse to find cheese?

7.5 min to nai :(?