Choose a number $n$ uniformly at random from the set $\{1,2, \ldots, 100\}$. Choose one of the first seven days of the year $2014$ at random and consider $n$ consecutive days starting from the chosen day. What is the probability that among the chosen $n$ days, the number of Sundays is different from the number of Mondays?

Let $M$ be the maximum value of the product of two positive integers when their sum is $66$. Let the sample space $S=\left\{x \in Z: x(66-x) \geq \frac{5}{9} M\right\}$ and the event $A=\{ x \in S : x$ is a multiple of $3$ $\}$. Then $P ( A )$ is equal to

One card is drawn from a well shuffled deck of $52$ cards. If each outcome is equally likely, calculate the probability that the card will be a diamond not an ace

One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.

A coin is tossed twice, what is the probability that atleast one tail occurs ?

The probability that a marksman will hit a target is given as $1/5$. Then his probability of at least one hit in $10$ shots, is