Solution:

Bookkeeper (00 kk ee)

Solution:

1/3

This is a famous question in understanding conditional probability, which simply means that given some information you might be able to get a better estimate.

The following are possible combinations of two children that form a sample space in any earthly family:

Boy - Girl
Girl - Boy
Boy - Boy
Girl - Girl

Since we know one of the children is a boy, we will drop the girl-girl possibility from the sample space.
This leaves only three possibilities, one of which is two boys. Hence the probability is 1/3

Solution:

Twinkle and Rinki start on opposite sides of the river

Solution:

1st person : Colin
2nd person : Rooney

They both lied.(I said at-least)
(If only one lied they would both be boys or both be girls)

Solution:

Only twenty-three people need be in the room, a surprisingly small number. The probability that there will not be two matching birthdays is then, ignoring leap years, 365x364x363x...x343/365 over 23 which is approximately 0.493. this is less than half, and therefore the probability that a pair occurs is greater than 50-50. With as few as fourteen people in the room the chances are better than 50-50 that a pair will have birthdays on the same day or on consecutive days.

Solution:

Throw the ball straight up in the air.

Solution:

Let us add the digits:
2 + 7 + 1 + 6 = 16
4 + 1 + 3 + 5 = 13
5 + 3 + 2 + 1 = 11
7 + 1 + 4 + 5 = 17

As you can see, only 2716 is a number whose digits add up to be a non prime number. Thus it is the odd one out.

Solution:

If all other conditions are fair, then the toss will generate a 52:48 distribution in the favor of heads. The toss boas factor will then be 52/48.

Using the same approach, if the coin will generate a 49:51 distribution in the favor of tails, the coin bias factor for heads will be 49/51.

Using the results, we can say that the combined bias factor is (52 * 49) / (51 * 48) = 2548 / 2448 which can be canceled if the floor bias factor is 2448 / 2548. The floor will generate a distribution factor of 2448 / (2558 + 2448) : 2548 + 2448) in favor of tails. If you calculate roughly, it will be 51.00080064% tails.

Solution:

According to the given data,

6 x number of notebooks + 5 x number of notepads = 32

Here, we are sure that the number of notebooks and the number of notepads can only result in whole numbers. Thus, the respective values will be 2 and 4.

Solution:

Let us rename the Five gallons basket and Three gallons basket as F and T.
Fill F completely and then pour to fill T completely. By doing this you have 2 gallons remaining in F. Pour out T entirely and then fill it with the remaining liquid from F. Now, T has 2 gallons of liquid.
Fill F fully again. Now pour the liquid to fill T which has just 1 gallons of capacity remaining. By doing this, you are left with the required 4 gallons of liquid in F.