The first box has two white balls. The second box has two black balls. The third box has a white and a black ball.

Boxes are labeled but all labels are wrong!

You are allowed to open one box, pick one ball at random, see its color and put it back into the box, without seeing the color of the other ball.

How many such operations are necessary to correctly label the boxes?

Solution:-

open the mix container and check!

If it’s black, the white ones are on the black label and the mix is in the white label

If it’s white, the black ones are on the white label and the mix is in the black label

It cannot be a mix under the mix label as all labels are WRONG!

b.There was a blind man. He had four socks in his drawer either black or white. He opened it and took out two socks. Now the probability that it was a pair of white socks is 1/2.

Can you find out the probability that he had taken out a pair of black socks ?

solution:-

This question can be a tricky one. The probability that is asked will be zero.

If the probability off taking out a pair of white socks is 1/2, it means that there is no black pair. This is because if there had been, there would have been three cases – white pair, black pair and mixed pair. But since in the question it is clear that there were just two chances (1/2), we can fairly deduce that there were only one black sock and the rest were white.

c.A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

solution:-

Let us solve this question one step at a time.

We know that each time the ball is dropped it bounces back and reach 2/3 of the height.

Thus, after the first bounce, the ball will reach 2/3 of the height from which it was dropped.

After the second bounce, the ball will reach 2/3 of the height again after the first bounce.

Thus the total height at which the ball must have reached by this time will be 2/3 * 2/3 = 4/9 of the original height.

After third bounce, 2/3 * 2/3 * 2/3 = 8/27 of the original height.

After fourth bounce, 2/3 * 2/3 * 2/3 * 2/3 = 16/81 of the original height.

Thus, the ball will reach 16/81 of the original height from which it was dropped.

d.You have 8 balls of same size and same shapes but one of them is heavier,you have only two chance to weight heavier ball?What would you do?

solution:-

At first we divide 8 balls into 3 ,3,2 and then we will weigh 3 and 3 balls if they equal we will now divide 2 balls into one and then we can know which one is heavier.2nd condition if one of the three balls is heavier now we keep one ball aside and weigh 2 balls if they equal the seperated ball is heavier and if not we will divide two balls and can seperate which one is heavier.

e.A snail is at the bottom of a 30 foot well. Every hour the snail is able to climb up 3 feet, then immediately slide back down 2 feet. How many hours does it take for the snail to get out of the well?

Solution:-

28 hours. The snail is travelling at one foot per hour, except on the 28^{th} hour the snail has already reached the top of the well, so it will not slide down the 2 feet.

f.There are 3 light bulbs in a hidden room and 3 switches outside the room that correspond to those light bulbs. You do not know which switch affects which bulb and you cannot see inside of the room. You are allowed to go inside of the room only one time. How do you find out which switch corresponds to which bulb?

solution:-

Turn on two switches and wait for a while. Then turn off one switch and go inside the room. The bulb that is still on corresponds to the switch that is still on. Touch the remaining bulbs. The hotter bulb is the switch that you turned off, and the remaining bulb is the switch that you never turned on.

g.Having an infinite supply of water and two containers, one for 3 liters and one for 5 liters, how would you measure 4 liters?

solution:-

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