[e-rutz]

Originally Posted by divishth

Answer is 1-(125/216) = 0.42
Probability That you will win = 1 - (Your Number would not come) = 1 - (5*5*5/6*6*6) = 91/216 = 0.42

But the problem asks what is the probability of winning money, not merely getting the desired number on the dice. Every event has some weightage.
So we have to calculate the probability that the man earns more money than he loses.

Probability of getting the no. on all 3 dice = 1/6* 1/6 * 1/6 = 1/216
Probability of getting the no. on only 2 dice = (1/6* 1/6 * 5/6) + (1/6* 5/6 * 1/6) +(5/6* 1/6 * 1/6) = 15/216
Probability of getting the no. on only 1 die = (1/6* 5/6 * 5/6) + (5/6* 1/6 * 5/6) +(5/6* 5/6 * 1/6) = 75/216

1/216 + 15/216 + 75/216 = 91/ 216 = 1 - (125/216)

The point is, in 216 trials the man (ideally) wins €3*1 + €2*15 + €1*75 = €108.
but he loses €1*125 = 125€. Essentially, the man never wins money? ABsurd....??
Can someone help?

[paradoxical123]

Can somebody please solve this question:

Twenty-seven identical white cubes are assembled into a single cube, the outside of which is painted black. The cube is then disassembled and the smaller cubes thoroughly shuffled in a bag. A blindfolded man (who cannot feel the paint) reassembles the pieces into a cube. What is the probability that the outside of this cube is completely black?

It has been solved before, but am not convinced with the solution provided.

[divishth]

Originally Posted by paradoxical123

Can somebody please solve this question:

Twenty-seven identical white cubes are assembled into a single cube, the outside of which is painted black. The cube is then disassembled and the smaller cubes thoroughly shuffled in a bag. A blindfolded man (who cannot feel the paint) reassembles the pieces into a cube. What is the probability that the outside of this cube is completely black?

It has been solved before, but am not convinced with the solution provided.

Let Number of possible correct re-arrangements be m = 3^8 * 8! * 2^12 * 12! * 4^6 * 6! * 24
Let Total Number of Possible Re-Arrangements be n = 24^27 * 27!

Probability = m/n

[paradoxical123]

How did you get that? Shouldn't total number of arrangements possible be 27 * (6 * 26C6) * (8 * 20C12) * (8 * 8C ??

As the cube that has no side painted can be placed in 27 ways.

The 6 cubes with exactly one face painted can be arranged in remaining 26 slots in 26C6 ways and since each of these cubes can have 6 possible orientations depending on in which direction the painted face points, we get 6 * 26C6.

Now we still have 20 slots left. The 12 cubes with 2 faces painted can be placed in 20C12 ways and each of these cubes can have 8 possible orientations, hence 8 * 20C12.

Finally, the remaining 8 cubes can be placed in 8C8 * 8 ways.

What is wrong with this reasoning?

[ansh.python]

gud 1......

[rohit_coep]

1. Mother Dairy sells milk packets in boxes of different sizes to its vendors. The vendors are charged Rs. 20 per packet up to 2000 packets in a box. Additions can be made only in a lot size of 200 packets. Each addition of one lot to the box results in a discount of one rupee an all the packets in the box. What should be the maximum size of the box that would maximize the revenue per box for Mother Dairy?

A. 2400 packets
B. 3000 packets
C. 4000 packets
D. None of the above.

2. If n + 2C8 : n – 2P4 = 57 : 16, then n =
A. 20
B. 22
C. 15
D. None of the above

3. A ladder 25 meters long is placed against a wall with its foot 7 meters away from the foot of the wall. How far should the foot be drawn out so that the top of the ladder may come down by half the distance of the total distance if the foot is drawn out?
A. 6 meters
B. 8 meters
C. 8.75 meters
D. None of the above

4. A pole has to be erected on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:
A. 8 metres
B. 8.25 metres
C. 5 metres
D. None of the above

Puys, please provide explanations as well.

Thanks,
Rohit.

[akshaymoon]

please help me solve these questions for STD and time & work...

1.there are two cities P & Q .A car A starts from city P at 6 am an reaches city Q at noon.Another car B starts from city Q at 7 am and reaches city P at 3 pm.
find the approximate time taken by the two cars to meet each other after car A starts.
a) 2 hr 51 mins b)3 hr 51 mins c) 2 hr 48 mins d) 3 hr 48 mins


2.A group of men , all of equal capacities were hired to work for Rs.10000. from this group one man started work, second day one more man joined him and like this every day one more men joined the group . if every men worked half their capacities then the work was completed exactly in 15 days . find the maximum amount earned by any man in the group?
a) Rs.750 b) Rs.1250 c) Rs 1500 d) none of these

[san.rahul99]

Originally Posted by rohit_coep

1. Mother Dairy sells milk packets in boxes of different sizes to its vendors. The vendors are charged Rs. 20 per packet up to 2000 packets in a box. Additions can be made only in a lot size of 200 packets. Each addition of one lot to the box results in a discount of one rupee an all the packets in the box. What should be the maximum size of the box that would maximize the revenue per box for Mother Dairy?

A. 2400 packets
B. 3000 packets
C. 4000 packets
D. None of the above.

Well start doing it from options...

2000 packets * Rs. 20 per packet = Rs. 40000

2200 * 19 = 41800

2400 * 18 = 43200

2600 * 17 = 44200

3000 * 15 = 45000

3200 * 14 = 44800
.
....so after 3000 it'll starts decreasing

Originally Posted by rohit_coep

4. A pole has to be erected on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:
A. 8 metres
B. 8.25 metres
C. 5 metres
D. None of the above

Puys, please provide explanations as well.

Thanks,
Rohit.

I have attached d figure of this ques with d post...
so according to the figure...

(a-b) = 7

also...
=) a^2 + b^2 = 13^2
=) (a-b)^2 + 2*a*b = 169
=) 7^2 + 2*a*b = 169
=) a*b = 60

by observing the factors of 60 n d the equation (a-b) = 7...v can say dat a=12 and b=5...

so the only answer option available is 5 metres...


P.S.:: puys pls solve other two ques...not understanding the last line of trigo ques n P&C kills me...

P.P.S:: sorry for the bad use of beautiful paint brush...

Untitled.jpg

[jaisriram]

solve and give explanation:

Two identical Re. 1 coins are kept on a table touching each other. One of the coins is fixed on the table whereas the other coin rolls (without sliding) along the periphery of the fixed coin, touching it at all times. How many complete rotations does the rolling coin make, when it reaches its initial position again for the first time?

[divishth]

Originally Posted by jaisriram

solve and give explanation:

Two identical Re. 1 coins are kept on a table touching each other. One of the coins is fixed on the table whereas the other coin rolls (without sliding) along the periphery of the fixed coin, touching it at all times. How many complete rotations does the rolling coin make, when it reaches its initial position again for the first time?

They will rotate 2 Times