Exercise-1

Three of the six vertices of a regular hexagon are chosen at random. Then the probability that the triangle with three vertices is equilateral is $\text{'}p\text{'}$ then $100 p$ equals

Four persons draw four cards form an ordinary pack of $52$ cards. Find the probability that no two cards are of equal value.

Box -I contains $5$ red and $2$ blue balls while box -II contains $2$ red and $6$ blue balls. A fair coin is tossed. If it turns up head, a ball is drawn from box-I, else a ball is drawn from box-ll. Find the probability of ball drawn is from box-I if it is blue.

Box$-\text{I}$ contains $5$ red and $2$ blue balls while box $-\text{II}$ contains $2$ red and $6$ blue balls. A fair coin is tossed. If it turns up head, a ball is drawn from box-I, else a ball is drawn from box-ll. Find the probability that a ball drawn is from bag$-\text{I}$ if it is blue.

A coin is tossed $n$ times, what is the chance that the head will present itself an odd number of times.

From a bag containing $2$ one rupee and $3$ two rupee coins. A person is allowed to draw $2$ coins randomly, then the value of his expectation.

$A$ & $B$ throw with one dice for a stake of $\text{Rs. }99/-$ which is to be won by the player who first throws $4$. If $A$ has the first throw then their respective expectations of rupees are:

A fair coin is tossed $99$ times. If $X$ is the number of times heads occur, if $P(X=r)$ is maximum then sum of possible values of $r$ is