Official Quant thread for CAT 2013

@pankaj1988 said:
A bag contains 3 Red, 2 Green and 4 Yellow balls. A ball is drawn and if it is Red or Yellow it is replaced otherwise not. Find the probability that second ball drawn is a yellow ball.
37/81?

GY = 2/9 * 4/8 = 1/9
RY = 3/9 * 4/9 = 4/27
YY = 4/9 * 4/9 = 16/81

Total = (9 +12 + 16)/81 = 37/81
@pankaj1988 said:
A bag contains 3 Red, 2 Green and 4 Yellow balls. A ball is drawn and if it is Red or Yellow it is replaced otherwise not. Find the probability that second ball drawn is a yellow ball.
37/81
@19rsb said:
Ravan has hundred sons.He takes every 10 sons to a jungle for hunting with no ten being repeated.Let X be the number of times that Ravan goes to the jungle and Y be the number of times that each son goes to the jungle.Find X-Y.
100c10-99c9??
@pankaj1988 37/81
@19rsb said:
Ravan has hundred sons.He takes every 10 sons to a jungle for hunting with no ten being repeated.Let X be the number of times that Ravan goes to the jungle and Y be the number of times that each son goes to the jungle.Find X-Y.
number of times ravan goes to jungle = C(100,10)
number of time a son goes to jungle = C(99,9)

hence X-Y = 99!/(90!*8!).

ATDH.
@pankaj1988 said:
A bag contains 3 Red, 2 Green and 4 Yellow balls. A ball is drawn and if it is Red or Yellow it is replaced otherwise not. Find the probability that second ball drawn is a yellow ball.
37/81?
@19rsb said:
Ravan has hundred sons.He takes every 10 sons to a jungle for hunting with no ten being repeated.Let X be the number of times that Ravan goes to the jungle and Y be the number of times that each son goes to the jungle.Find X-Y.
100C10 - 99C9

For every combination of 10 sons
X = Number of times Ravan goes to the jungle = 100C10 (select 10 out of 100)

Y = Number of times each son goes to the jungle = 99C9 (select 9 out of 99)

X - Y = 100C10 - 99C9
@pankaj1988 said:
A bag contains 3 Red, 2 Green and 4 Yellow balls. A ball is drawn and if it is Red or Yellow it is replaced otherwise not. Find the probability that second ball drawn is a yellow ball.
37/81
@pankaj1988 said:
A bag contains 3 Red, 2 Green and 4 Yellow balls. A ball is drawn and if it is Red or Yellow it is replaced otherwise not. Find the probability that second ball drawn is a yellow ball.
7/9*4/9 + 2/9*4/8 = 37/81 ?
@pankaj1988 said:
A bag contains 3 Red, 2 Green and 4 Yellow balls. A ball is drawn and if it is Red or Yellow it is replaced otherwise not. Find the probability that second ball drawn is a yellow ball.
Edit: Can you please explain this:
Ball is replaced if it is red or yellow..that means we draw the second ball only if 1st is green...
So why are we taking RY and YY ??
@ScareCrow28 said:
Edit: Can you please explain this:Ball is replaced if it is red or yellow..that means we draw the second ball only if 1st is green...So why are we taking RY and YY ??
3R 2G aur 4Y hai. So if you take out 1 ball and that is red/yellow, you replenish it once again. If it is green, you do not replenish it. That means if you pick R/Y as 1st ball, you will have 9 left during the second ball draw. If you picked a green one in the first case, you have 8 balls left for the second draw 😃
@pankaj1988 said:
A, B and C in order, toss a coin. The one who gets a head first wins. Find their respective probabilities of winning.
4/7,2/7,1/7
@ScareCrow28 said:
Edit: Can you please explain this:Ball is replaced if it is red or yellow..that means we draw the second ball only if 1st is green...So why are we taking RY and YY ??
drawn is different from taking out .
A ball is said to be drawn even if it is replaced afterwards .
@ayushnasa said:
3R 2G aur 4Y hai. So if you take out 1 ball and that is red/yellow, you replenish it once again. If it is green, you do not replemish it. That means if you pick R/Y as 1st ball, you will have 9 left during the second ball draw. If you picked a green one in the first case, you have 8 balls left for the second draw
No... what i am asking is.. If the 1st ball is red/yellow, it is replaced...that means the ball is again put into the bag and again the 1st one is taken out... So we take out the 2nd ball only if 1st is green na?? If it's not green then we keep on taking out 1st ball again n again?
@ScareCrow28 said:
Edit: Can you please explain this:Ball is replaced if it is red or yellow..that means we draw the second ball only if 1st is green...So why are we taking RY and YY ??
Bhai I guess u misinterpreted the ques...got to take ball in 2nd step irrespective of the first step...In the first step if the ball is red or yellow u don't take any ball out...
@ScareCrow28 said:
No... what i am asking is.. If the 1st ball is red/yellow, it is replaced...that means the ball is again put into the bag and again the 1st one is taken out... So we take out the 2nd ball only if 1st is green na?? If it's not green then we keep on taking out 1st ball again n again?
A bag contains 3 Red, 2 Green and 4 Yellow balls. A ball is drawn and if it is Red or Yellow it is replaced otherwise not. Find the probability that second ball drawn is a yellow ball.

No no... The ball you take out the second time is the "second ball drawn".. :)
@ScareCrow28 said:
No... what i am asking is.. If the 1st ball is red/yellow, it is replaced...that means the ball is again put into the bag and again the 1st one is taken out... So we take out the 2nd ball only if 1st is green na?? If it's not green then we keep on taking out 1st ball again n again?
Bhai, leave the ball in the bag before picking up the second one please. Warna to obviously wahi uthate rahoge :mg:
@ScareCrow28 said:
A,B,C started to reach varanasi from delhi 300 km away they have only one bike which travel at a speed of 60 km/hr and every one can walk at a speed of 15 km/hr condition is every one has to reach at the same time and only two person can travel on the bike at the same time. wat is the minimum time required for them to reach there.P.S. All of them start at same time and onlyA can drive the bikeP.P.S.. : Question was posted yesterday..but i Couldn't reach to the answer matching with OAJAAGO GRAHAK JAAGO PPPS : I Got the answer now
I found a very interesting solution to this problem using the idea of symmetry.

Since there are two people walking reach the destination at the same time hence their average speeds must be same => the time they spend on bike and the time they spend walking also must be same. => distance both B and C walk also must be same, say x.

Logical Part
Say person B walks a distance x initially and then gets on the bike....and C first goes on the bike and then walks distance x.

Now in this process biker drops B at a distance x from Varanasi and goes back and picks C and still manages to reach varanasi at the same time B. This implies Biker covered 4 times the distance (as his speed is 4 times) in process of going back and picking up C and then going to varanasi. Hence we get a diagram like below

------x------(A picks C)--------------(3x/2)-------------(A drops B here)--------x--------

Calculations

Hence x+3x/2 + x = 300 => x = 600/7

Now time taken for B = (x+3x/2) on bike and last x by foot.
=> t = (5/2)*(600/7)/60 + (600/7)/15 = 65/7 Hrs.

ATDH.


@anytomdickandhary said:
I found a very interesting solution to this problem using the idea of symmetry. Since there are two people walking at the same speed there is no reason why they should walk for different distance so as to achieve minimum time. Logical PartSay person B walks a distance x initially and then gets on the bike....and C first goes on the bike and then walks distance x.Now in this process biker drops B at a distance x from Varanasi and goes back and picks C and still manages to reach varanasi at the same time B. This implies Biker covered 4 times the distance (as his speed is 4 times) in process of going back and picking up C and then going to varanasi. Hence we get a diagram like below------x------(A picks C)--------------(3x/2)-------------(A drops B here)--------x--------CalculationsHence x+3x/2 + x = 300 => x = 600/7Now time taken for B = (x+3x/2) on bike and last x by foot. => t = (5/2)*(600/7)/60 + (600/7)/15 = 65/7 Hrs.ATDH.
\\____O// Prabhu
@ayushnasa said:
Bhai, leave the ball in the bag before picking up the second one please. Warna to obviously wahi uthate rahoge
@grkkrg said:
A bag contains 3 Red, 2 Green and 4 Yellow balls. A ball is drawn and if it is Red or Yellow it is replaced otherwise not. Find the probability that second ball drawn is a yellow ball.No no... The ball you take out the second time is the "second ball drawn"..
@pankaj1988 said:
Bhai I guess u misinterpreted the ques...got to take ball in 2nd step irrespective of the first step...In the first step if the ball is red or yellow u don't take any ball out...
@rubikmath said:
drawn is different from taking out .A ball is said to be drawn even if it is replaced afterwards .
YO!!! These many PUYS can't be wrong at the same time!! I got it now! :P