## Thursday, 10 October 2013

### Coin Tossing Experiment

Consider a coin tossing experiment. Let X be the number of heads if you toss a coin for 99 times. Let Y be the number of heads if you toss a coin for 100 times. What is the probability that X is less than Y?

## Tuesday, 17 September 2013

### Prime Numbers

How many prime numbers exist between 2 consecutive prime numbers?

### House with too many doors

Have a look at the house plan at the right hand side, with five rooms and sixteen doors in total. The intention is to make a run through the rooms and pass each of the sixteen doors exactly once.
How many ways can it be done?

## Saturday, 14 September 2013

### Color the Cube

Given the cube and 2 colors such that each color is on exactly 3 faces, how many different coloring combinations are possible?

### Taxi Service

Mr. Kothari runs a taxi service in Ahmedabad. Every day, he travels from Ahmedabad to one nearby city and back. All the cities are less than 100 km away from Ahmedabad. Everyday morning, Mr. Kothari fills his car’s fuel tank to the brim. On a full tank, the car can travel maximum 250 km. Unfortunately, Mr. Kothari forgot to fill his tank today. What is the probability that he will run out of fuel during the day?