Easy | Probability |

How do you place 50 good candies and 50 rotten candies in two boxes such that if you choose a box at random and take out a candy at random, it better be good!

That means probability of choosing a good candy should be highest.

That means probability of choosing a good candy should be highest.

Hint

Placing all bad in 1 box and all good in another will give probability of choosing good just half. But placing only one type of candy in one box makes sure that good candy has a probability of at-least 1/2

Answer

Put 1 good candy in one box and all other (49 good and 50 rotten candies) in second box

Solution

Put 1 good candy in one box and all other (49 good and 50 rotten candies) in second box. This will give a probability of (1/2)*1 + (1/2)*(49/100) = 74.5%

Easy | Probability |

In a world where everyone wants a girl child, each family continues having babies till they have a girl. What do you think will the boy to girl ratio be eventually? (Assuming probability of having a boy or a girl is the same)

Answer

1:1

Solution

Suppose there are N couples. First time, N/2 girls and N/2 boys are born (ignoring aberrations). N/2 couples retire, and rest half try another child. Next time, N/4 couples give birth to N/4 girls and rest N/4 boys. Thus, even in second iteration, ratio is 1:1. It can now be seen that this ratio always remain same, no matter how many times people try to give birth to a favored gender.

Easy | Strategy |

Hundred tigers and one sheep are put on a magic island that only has grass. Tigers can live on grass, but they want to eat sheep. If a Tiger bites the Sheep then it will become a sheep itself. If 2 tigers attack a sheep, only the first tiger to bite converts into a sheep. Tigers don’t mind being a sheep, but they have a risk of getting eaten by another tiger. All tigers are intelligent and want to survive. Will the sheep survive?

Hint

Instead of 100, think of 1 or 2 tiger's case.

Answer

Sheep survives!

Solution

If there is 1 tiger, then it will eat the sheep because he does not need to worry about being eaten. Sheep will not survive.

If there are 2 tigers, both of them knows that if one eats the Sheep, the other tiger will eat him. So, the sheep will survive.

If there are 3 tigers, then they each of them knows that if one tiger eats up the sheep, then Iceland will be left with 1 sheep and 2 tigers and as shown in the previous case, the sheep will survive. Hence each tiger will try to eat up the sheep. The sheep will not survive.

If there are 4 tigers, then the sheep will survive.

And so on….

So, If there are even number of tigers the sheep will survive, else it will die. Hence, if there are 100 tigers the sheep will survive.

If there are 2 tigers, both of them knows that if one eats the Sheep, the other tiger will eat him. So, the sheep will survive.

If there are 3 tigers, then they each of them knows that if one tiger eats up the sheep, then Iceland will be left with 1 sheep and 2 tigers and as shown in the previous case, the sheep will survive. Hence each tiger will try to eat up the sheep. The sheep will not survive.

If there are 4 tigers, then the sheep will survive.

And so on….

So, If there are even number of tigers the sheep will survive, else it will die. Hence, if there are 100 tigers the sheep will survive.

Source: Common

Enable Like and Comment Easy | Strategy |

A duck is swimming at the center of a circular lake. A fox is waiting at the shore, not able to swim, willing to eat the duck. It may move around the whole lake with a speed four times faster than the duck can swim. As soon as duck reaches the surface, it can fly, but not within the pond. Can the duck always reach the shore without being eaten by the fox?

Hint

Fox is chasing duck brainlessly. If duck's angular velocity is (somehow) more than fox, duck may actually create some sort of phase lag.

Solution

At radius of slightly less than r/4 the duck can swim in circles, forcing the fox to run around. once the duck is at a phase of pi from fox it starts swimming towards the shore and flies.

Source: Technical Interview

Enable Like and Comment Easy | General |

An airplane flies in a straight line from airport A to airport B, then back in a straight line from B to A. It travels with a constant engine speed and there is no wind. Will its travel time for the same round trip be greater, less or the same if, throughout both flights, at the same engine speed, a constant wind blows from A to B?

Answer

Wind will always slow down the journey!

Solution

The time during which the plane's speed is boosted is shorter than the time during which it is retarded, so the over-all effect is of retardation. Consider the example when plane's speed is same as wind. In one direction, plane's speed doubles, while in the other, it becomes zero! (i.e. it takes infinte time to finish the journey!)

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